Maple Calculation for Reese

Please note that the format got messed up when I copied it here, in particular, the exponents moved to the front and are not with the factors anymore!  Note the extra 3s and 4s and other factors in front (the lines should begin with 5, 9, 13, 17, 21, etc.  Not sure how easy it will be for you to match the exponents to the correct factors,  but I hope it is still mostly readable.

> with(numtheory);
[GIgcd, bigomega, cfrac, cfracpol, cyclotomic, divisors, factorEQ, factorset, fermat, imagunit, index, integral_basis, invcfrac, invphi, issqrfree, jacobi, kronecker, lambda, legendre, mcombine, mersenne, migcdex, minkowski, mipolys, mlog, mobius, mroot, msqrt, nearestp, nthconver, nthdenom, nthnumer, nthpow, order, pdexpand, phi, pi, pprimroot, primroot, quadres, rootsunity, safeprime, sigma, sq2factor, sum2sqr, tau, thue]> print();
[GIgcd, bigomega, cfrac, cfracpol, cyclotomic, divisors, factorEQ, factorset, fermat, imagunit, index, integral_basis, invcfrac, invphi, issqrfree, jacobi, kronecker, lambda, legendre, mcombine, mersenne, migcdex, minkowski, mipolys, mlog, mobius, mroot, msqrt, nearestp, nthconver, nthdenom, nthnumer, nthpow, order, pdexpand, phi, pi, pprimroot, primroot, quadres, rootsunity, safeprime, sigma, sq2factor, sum2sqr, tau, thue]
> a := cfrac(sqrt(3), 499);
> nthconver(a, 299);
30981478142922605786470911716889490605847633087781492960023267065992810797375\ 088343751/17887164745708873375475119570168861054076647466929665349269183748\ 377915029312001619500

> for j to 10 do n := nthnumer(a, 4*j+1); m := (1/4*n^2-1)*(1/3); print(4*j+1, n, m, ifactor(m, easy)) end do;
3 5, 26, 56, (2) (7)
3 9, 362, 10920, (2) (3) (5) (7) (13)
4 13, 5042, 2118480, (2) (3) (5) (7) (13) (97)
4 17, 70226, 410974256, (2) (7) (11) (19) (97) (181)
3 21, 978122, 79726887240, (2) (3) (5) (7) (11) (13) (19) (181) (193)
3 25, 13623482, 15466605150360, (2) (3) (5) (7) (13) (41) (71) (193) (2521)
5 29, 189750626, 3000441672282656, (2) (7) (31) (41) (71) (97) (607) (2521)
33, 2642885282, 582070217817684960, 5 2 (2) (3) (5) (7) (13) (17) (31) (37) (53) (73) (97) (607)
37, 36810643322, 112918621814958599640, 3 2 (2) (3) (5) (7) (11) (13) (17) (19) (37) (53) (73) (181) (37441)
41, 512706121226, 21905630561884150645256, 3 (2) (7) (11) (19) (23) (43) (181) (571) (489061) (37441)

> for j from 10 to 249 do n := nthnumer(a, 4*j+1); m := (1/4*n^2-1)*(1/3); print(4*j+1, ifactor(m, easy)) end do;
3 41, (2) (7) (11) (19) (23) (43) (181) (571) (489061) (37441)
4 45, (2) (3) (5) (7) (13) (23) (43) (97) (193) (571) (489061) (37633)
4 49, (2) (3) (5) (7) (13) (97) (193) (6811741) (2131) (3691) (37633)
3 2 53, (2) (7) (41) (71) (337) (6811741) (2131) (3691) (3079) (2521)
3 2 2 57, (2) (3) (5) (7) (11) (13) (19) (29) (41) (61) (71) (181) (241) (337) ( 661) (3079) (2521)
6 2 61, (2) (3) (5) (7) (11) (13) (19) (29) (31) (61) (97) (181) (241) (607) (661 ) (708158977)
6 65, (2) (7) (31) (67) (97) (101) (443) (509) (607) (708158977) (1321442641)
3 2 69, (2) (3) (5) (7) (13) (17) (37) (53) (67) (73) (101) (193) (443) (509) ( 1321442641) (7300801)
3 2 73, (2) (3) (5) (7) (13) (17) (37) (53) (73) (193) (18405321661) (191861) ( 110771) (7300801)
4 77, (2) (7) (11) (19) (79) (97) (181) (17927599) (18405321661) (191861) ( 110771) (37441)
4 81, (2) (3) (5) (7) (11) (13) (19) (41) (71) (79) (97) (181) (757) (17927599) (10333) (37441) (2521) (3361) (2017)
3 85, (2) (3) (5) (7) (13) (23) (41) (43) (71) (571) (757) (273349327681) (10333 ) (489061) (2521) (3361) (2017)
3 89, (2) (7) (23) (43) (47) (277) (571) (4244329) (273349327681) (56857) ( 1542841) (3037) (489061)
5 93, (2) (3) (5) (7) (13) (31) (47) (97) (193) (277) (607) (1416317953) (4244\ 329) (56857) (1542841) (3037) (37633)
5 97, (2) (3) (5) (7) (11) (13) (19) (31) (97) (181) (193) (499) (607) (1049) ( 1416317953) (274757858101) (524899) (37633)
3 2 101, (2) (7) (11) (19) (103) (181) (499) (1049) (4998431569) (274757858101) (524899 ) (6811741) (2131) (3691)
3 3 2 105, (2) (3) (5) (7) (13) (17) (37) (53) (73) (103) (109) (1297) (4998431569 ) (140453) (6811741) (2131) (3691) (139537) (46817)
4 3 2 109, (2) (3) (5) (7) (13) (17) (37) (41) (53) (71) (73) (97) (109) (337) ( 1297) (12065089) (4417729) (140453) (139537) (46817) (3079) (2521)
4 2 113, (2) (7) (41) (59) (71) (97) (337) (349) (521) (3971200609) (138907099) (12065089 ) (4417729) (2609) (6961) (3079) (2521)
3 2 117, (2) (3) (5) (7) (11) (13) (19) (29) (59) (61) (181) (193) (241) (349) ( 521) (661) (1201) (3971200609) (1185361) (138907099) (2609) (6961) (37441)
3 2 121, (2) (3) (5) (7) (11) (13) (19) (29) (61) (181) (193) (241) (373) (661) (1201 ) (360250962984637) (37139) (1185361) (203857) (8059) (2543) (37441)
7 125, (2) (7) (31) (97) (127) (373) (607) _c40_2 (37139) (203857) (8059) (2543)
7 129, (2) (3) (5) (7) (13) (23) (31) (43) (97) (127) (571) (607) _c25_2 (150217 ) (1959673) (489061) (652081) (391249)
3 133, (2) (3) (5) (7) (13) (23) (43) (67) (101) (443) (509) (571) (5061296774\ 61847) (150217) (1959673) (1321442641) (489061) (652081) (391249) (3943)
3 137, (2) (7) (11) (19) (41) (67) (71) (101) (139) (181) (443) (509) _c29_2 ( 66499) (1321442641) (5352481) (2521) (3943)
4 2 141, (2) (3) (5) (7) (11) (13) (17) (19) (37) (41) (53) (71) (73) (97) (139) (181) (193) (57128490881281) (66499) (94329793) (565057) (5352481) (7300801) (37633) (2521)
4 2 145, (2) (3) (5) (7) (13) (17) (37) (53) (73) (97) (193) _c33_2 (94329793) ( 565057) (99901) (2221) (7300801) (37633)
3 149, (2) (7) (151) _c52_2 (18405321661) (191861) (110771) (99901) (2221)
3 2 153, (2) (3) (5) (7) (13) (151) (157) (313) _c19_2 (161149) (18405321661) ( 191861) (6811741) (5449393) (2131) (110771) (173629) (3691) (29017)
5 2 157, (2) (3) (5) (7) (11) (13) (19) (31) (79) (97) (157) (181) (313) (607) _c17_2 (161149) (710110879) (6811741) (5449393) (2131) (173629) (3691) (29017 ) (37441)
5 161, (2) (7) (11) (19) (31) (79) (83) (97) (163) (181) (607) _c53_2 (710110879 ) (367033) (37441)
3 2 165, (2) (3) (5) (7) (13) (41) (71) (83) (163) (193) (337) (757) _c50_3 ( 367033) (10333) (3079) (2521) (3361) (2017)
3 2 169, (2) (3) (5) (7) (13) (41) (71) (193) (337) (757) (859) _c50_4 (3527) ( 462337) (10333) (3079) (2521) (3361) (2017)
4 173, (2) (7) (23) (43) (97) (571) (859) _c51_2 (273349327681) (3527) (462337) (489061) (74052001)
4 2 2 177, (2) (3) (5) (7) (11) (13) (17) (19) (23) (29) (37) (43) (53) (61) (73) (89) (97) (181) (241) (571) (661) (1019420970495841) (83609) (273349327681) (5199301 ) (10255501) (489061) (7160401) (74052001)
3 2 2 181, (2) (3) (5) (7) (11) (13) (17) (19) (29) (37) (47) (53) (61) (73) (89) (181) (241) (277) (661) (919) (15854174700638744970919) (83609) (4244329) ( 5199301) (56857) (10255501) (1542841) (3037) (7160401)
3 185, (2) (7) (47) (277) (919) (1129) (1693) _c55_3 (847129) (4793) (4244329) (56857 ) (20399) (1542841) (3037)
6 189, (2) (3) (5) (7) (13) (31) (97) (193) (607) (769) (1129) (1693) _c61_3 ( 847129) (4793) (314113) (20399) (37633)
6 193, (2) (3) (5) (7) (13) (31) (41) (71) (97) (193) (491) (607) (769) _c68_4 (314113 ) (197569) (37633) (2521)
3 197, (2) (7) (11) (19) (41) (71) (181) (199) (491) (499) (1049) _c61_4 (2747\ 57858101) (524899) (37441) (197569) (2521)
3 201, (2) (3) (5) (7) (11) (13) (19) (67) (101) (181) (199) (409) (443) (499) (509 ) (613) (1049) (379357631304275170999) (8623081) (2957) (357509) (227257) ( 274757858101) (524899) (1321442641) (994093) (7753) (37441)
4 2 205, (2) (3) (5) (7) (13) (67) (97) (101) (103) (409) (443) (509) (613) _c16_2 (4998431569) (8623081) (2957) (357509) (227257) (2287) (112111) ( 1321442641) (6811741) (2131) (994093) (3691) (7753) (4993)
4 2 209, (2) (7) (97) (103) (107) (211) (1483) _c59_3 (4998431569) (4133) (2287) (112111) (6811741) (2131) (71233) (3691) (4993)
3 3 213, (2) (3) (5) (7) (13) (17) (37) (53) (73) (107) (109) (193) (211) (433) (1297 ) (1483) _c62_2 (4133) (140453) (71233) (139537) (46817) (7300801)
3 3 2 217, (2) (3) (5) (7) (11) (13) (17) (19) (23) (37) (43) (53) (73) (109) (181 ) (193) (433) (571) (1297) (1321) _c60_2 (140453) (139537) (489061) (46817) (7300801 )
5 2 2 221, (2) (7) (11) (19) (23) (31) (41) (43) (71) (97) (181) (223) (337) (571) (607) (1321) (1567) _c64_4 (12065089) (4417729) (489061) (3079) (2521)
5 2 225, (2) (3) (5) (7) (13) (31) (41) (71) (97) (113) (223) (229) (337) (457) (569 ) (607) (1567) _c37_2 (6269) (24730249) (12065089) (18405321661) (191861) ( 4417729) (110771) (381673) (3079) (2521)
3 229, (2) (3) (5) (7) (13) (59) (113) (229) (349) (457) (521) (569) _c48_2 ( 6269) (24730249) (138907099) (18405321661) (191861) (2609) (110771) (136417) (6961) (4177) (381673)
3 233, (2) (7) (59) (349) (353) (521) _c84_2 (138907099) (2609) (31153) (5783) (73751 ) (136417) (6961) (4177)
4 2 237, (2) (3) (5) (7) (11) (13) (19) (29) (61) (79) (97) (181) (193) (241) ( 353) (661) (1201) _c65_2 (1185361) (28042561) (31153) (5783) (73751) (37441) (37633) (20161)
4 2 241, (2) (3) (5) (7) (11) (13) (19) (29) (61) (79) (97) (181) (193) (241) ( 661) (733) (1097) (1201) _c64_5 (1185361) (250709) (23057) (28042561) (3539) (37441) (37633) (20161)
3 245, (2) (7) (373) (733) (1097) _c91_3 (37139) (21324529) (250709) (203857) ( 23057) (8059) (3539) (2543)
3 2 249, (2) (3) (5) (7) (13) (17) (37) (41) (53) (71) (73) (373) (757) _c55_4 ( 18269) (14046709069) (37139) (21324529) (203857) (8059) (1122157) (2543) ( 10333) (2393) (24697) (2521) (3361) (2017)
8 2 253, (2) (3) (5) (7) (13) (17) (31) (37) (41) (53) (71) (73) (97) (127) (607) (757) _c64_6 (22783) (18269) (14046709069) (592897) (1122157) (10333) (2393) (24697) (2521) (3361) (2017)
8 257, (2) (7) (11) (19) (31) (97) (127) (131) (181) (389) (607) _c102_3 (22783) (592897) (6811741) (2131) (3691)
3 261, (2) (3) (5) (7) (11) (13) (19) (23) (43) (131) (181) (193) (389) (571) _c68_5 (150217) (549649) (1959673) (273349327681) (6811741) (2131) (3691) ( 489061) (652081) (391249)
3 265, (2) (3) (5) (7) (13) (23) (43) (193) (571) _c68_6 (150217) (549649) ( 1959673) (273349327681) (28867621) (3407353) (89445401) (3217) (489061) ( 652081) (391249)
4 269, (2) (7) (67) (97) (101) (271) (443) (509) _c91_4 (28867621) (3407353) ( 89445401) (1321442641) (3217) (8161) (26113) (3943)
4 273, (2) (3) (5) (7) (13) (47) (67) (97) (101) (137) (271) (277) (443) (509) (829 ) (1657) _c59_4 (235013) (10397197) (4244329) (56857) (1321442641) (1542841) (12697) (86526553) (3037) (8161) (26113) (3943)
3 2 277, (2) (3) (5) (7) (11) (13) (19) (41) (47) (71) (137) (139) (181) (277) ( 337) (829) (1657) _c45_2 (66499) (61879) (235013) (10397197) (4244329) ( 1749889681) (56857) (5352481) (1542841) (12697) (86526553) (3037) (3079) ( 37441) (2521)
3 2 281, (2) (7) (11) (19) (41) (71) (139) (181) (283) (337) (853) (1277) _c79_2 (66499) (61879) (15349270753) (1749889681) (192553) (83497) (5352481) (3079) (37441) (2521)
5 2 285, (2) (3) (5) (7) (13) (17) (31) (37) (53) (73) (97) (193) (283) (577) ( 607) (853) (1153) (1277) _c70_2 (94329793) (15349270753) (565057) (192553) ( 83497) (7300801) (7489) (37633) (32257) (14401)
5 2 289, (2) (3) (5) (7) (13) (17) (31) (37) (53) (73) (97) (193) (577) (607) ( 1153) (1459) _c75_2 (881987) (94329793) (565057) (25491601) (1079233) (1753) (7300801) (7489) (37633) (32257) (14401)
293, 3 (2) (7) (1459) _c131_3 (881987) (25491601) (1079233) (1753) (99901) (2221)
3 3 297, (2) (3) (5) (7) (11) (13) (19) (29) (61) (149) (181) (241) (449) (499) (601 ) (661) (1049) _c92_2 (300945014701) (417389101) (274757858101) (524899) ( 99901) (2221)
4 3 301, (2) (3) (5) (7) (11) (13) (19) (29) (61) (97) (149) (151) (181) (241) ( 449) (499) (601) (661) (1049) _c77_2 (300945014701) (417389101) (274757858101 ) (524899) (18405321661) (191861) (110771)
4 305, (2) (7) (23) (41) (43) (71) (97) (151) (307) (461) (571) _c110_2 (7699) (18405321661 ) (191861) (1962577) (110771) (489061) (3697) (2521)
3 2 2 309, (2) (3) (5) (7) (13) (23) (41) (43) (71) (103) (157) (193) (307) (313) (461) (571) _c73_2 (7699) (4998431569) (161149) (6811741) (5449393) (2131) ( 1962577) (173629) (3691) (86113) (489061) (29017) (3697) (2521)
3 2 2 313, (2) (3) (5) (7) (13) (103) (157) (193) (313) _c99_2 (4998431569) ( 161149) (2306327) (21570793) (6811741) (5449393) (2131) (173629) (3691) ( 86113) (29017)
6 317, (2) (7) (11) (19) (31) (79) (97) (181) (607) _c131_4 (2306327) (710110879 ) (21570793) (7845121) (37441)
6 4 321, (2) (3) (5) (7) (11) (13) (17) (19) (31) (37) (53) (73) (79) (97) (109) (181) (607) (1297) _c96_4 (6317) (710110879) (7845121) (140453) (48681161) ( 122149) (75169) (139537) (46817) (37441)
3 4 325, (2) (3) (5) (7) (13) (17) (37) (53) (73) (83) (109) (163) (1297) _c122_3 (6317) (367033) (140453) (48681161) (122149) (75169) (139537) (46817)
3 329, (2) (7) (83) (163) (167) (331) (1493) _c157_2 (1206157) (367033) (45817)
4 2 333, (2) (3) (5) (7) (13) (41) (71) (97) (167) (193) (331) (337) (673) (757) (1493) _c114_3 (12065089) (1206157) (4417729) (45817) (10333) (3079) (37633) (2521) (3361) (2017)
4 2 337, (2) (3) (5) (7) (11) (13) (19) (41) (67) (71) (97) (101) (181) (193) ( 337) (443) (509) (673) (757) (1699) _c96_5 (12065089) (4417729) (336815051) (1321442641 ) (10333) (19381) (3079) (37633) (2521) (3361) (2017)
3 341, (2) (7) (11) (19) (67) (101) (181) (443) (509) (859) (1699) _c142_3 ( 336815051) (1321442641) (3527) (462337) (19381)
3 345, (2) (3) (5) (7) (13) (59) (173) (349) (521) (859) _c123_2 (43744993) ( 138907099) (1913) (2609) (140593) (3527) (462337) (38977) (6961) (1741) (2089 ) (151901)
5 349, (2) (3) (5) (7) (13) (23) (31) (43) (59) (97) (173) (349) (521) (571) ( 607) _c96_6 (43744993) (138907099) (1913) (273349327681) (2609) (140593) ( 38977) (6961) (1741) (2089) (489061) (74052001) (151901) (6337)
5 353, (2) (7) (23) (31) (43) (97) (179) (571) (607) _c137_2 (48239) (27334932\ 7681) (689929) (149521) (2137) (489061) (74052001) (6337)
3 2 2 357, (2) (3) (5) (7) (11) (13) (17) (19) (29) (37) (53) (61) (73) (89) (179) (181) (193) (241) (661) (1201) _c102_4 (83609) (1185361) (48239) (5199301) ( 689929) (149521) (2137) (10255501) (165601) (7160401) (7300801) (37441)
3 2 2 361, (2) (3) (5) (7) (11) (13) (17) (19) (29) (37) (41) (53) (61) (71) (73) (89) (181) (193) (241) (661) (1201) _c98_2 (83609) (1185361) (5199301) ( 6811741) (2131) (10255501) (3691) (165601) (7160401) (2003) (6553) (7300801) (37441) (2521)
4 365, (2) (7) (41) (47) (71) (97) (277) (367) (919) _c138_2 (4244329) (27207343 ) (56857) (6811741) (2131) (1542841) (3691) (3037) (2003) (6553) (2521)
4 369, (2) (3) (5) (7) (13) (47) (97) (277) (367) (373) (919) _c117_2 (37139) ( 25611457) (11029373085361) (4244329) (203857) (48733) (27207343) (56857) ( 8059) (1542841) (2543) (3037) (5953)
3 373, (2) (3) (5) (7) (13) (373) (1129) (1693) _c140_2 (847129) (37139) (4793) (25611457) (11029373085361) (203857) (48733) (8059) (20399) (2543) (5953)
3 2 377, (2) (7) (11) (19) (181) (191) (379) (1129) (1693) _c152_2 (847129) (4793 ) (18405321661) (191861) (2070241) (110771) (20399) (2281)
7 2 381, (2) (3) (5) (7) (11) (13) (19) (31) (97) (127) (181) (191) (193) (379) (607 ) (769) _c143_2 (314113) (18405321661) (191861) (2070241) (110771) (81409) ( 2281) (37633)
7 385, (2) (3) (5) (7) (13) (31) (97) (127) (193) (607) (769) (971) _c169_3 ( 2145279937) (314113) (16103) (81409) (37633)
3 3 389, (2) (7) (41) (71) (337) (491) (971) _c175_2 (2145279937) (16103) (811441 ) (3079) (197569) (2521)
3 2 3 393, (2) (3) (5) (7) (13) (17) (23) (37) (41) (43) (53) (71) (73) (197) (337 ) (397) (491) (571) _c122_4 (1166617) (150217) (1959673) (146790818637606001) (811441) (489061) (652081) (391249) (3079) (197569) (2521)
4 2 397, (2) (3) (5) (7) (11) (13) (17) (19) (23) (37) (43) (53) (73) (79) (97) (181 ) (197) (199) (397) (499) (571) (1049) _c115_2 (1166617) (150217) (1959673) (146790818637606001 ) (274757858101) (524899) (489061) (652081) (391249) (37441)
4 401, (2) (7) (11) (19) (79) (97) (181) (199) (499) (1049) (1213) _c161_2 ( 8688917689) (7818473833) (274757858101) (524899) (53731) (37441)
3 405, (2) (3) (5) (7) (13) (67) (101) (193) (409) (443) (509) (613) (1213) _c128_2 (8688917689) (8623081) (7818473833) (2957) (357509) (227257) (230929) (53731) (1321442641) (994093) (271729) (7753) (3943)
3 409, (2) (3) (5) (7) (13) (67) (101) (193) (409) (443) (509) (613) (1237) _c141_2 (399304427) (8623081) (2957) (357509) (227257) (230929) (123601) ( 1321442641) (994093) (271729) (7753) (3943)
5 2 413, (2) (7) (31) (97) (103) (607) (1237) _c171_2 (399304427) (4998431569) ( 2287) (123601) (112111) (6811741) (2131) (3691) (4993)
5 2 2 417, (2) (3) (5) (7) (11) (13) (19) (29) (31) (41) (61) (71) (97) (103) (139 ) (181) (241) (421) (607) (661) (757) _c114_4 (66499) (4998431569) (136709) (2287 ) (112111) (105109201) (6811741) (2131) (5352481) (10333) (3691) (4993) (4621 ) (408241) (2521) (3361) (2017)
3 2 421, (2) (3) (5) (7) (11) (13) (19) (29) (41) (61) (71) (107) (139) (181) ( 211) (241) (421) (661) (757) (1483) _c134_2 (66499) (4133) (3640193911) ( 136709) (105109201) (5352481) (71233) (10333) (4663) (4621) (408241) (2521) (3361 ) (2017)
3 425, (2) (7) (107) (211) (1483) _c195_2 (4133) (96220393) (3640193911) (12841) (51361) (71233) (4663)
4 3 429, (2) (3) (5) (7) (13) (17) (37) (53) (73) (97) (109) (193) (433) (1297) _c156_3 (94329793) (96220393) (39274849) (565057) (140453) (12841) (51361) ( 139537) (46817) (7300801) (37633)
4 3 433, (2) (3) (5) (7) (13) (17) (37) (53) (73) (97) (109) (193) (433) (653) ( 1297) _c156_4 (94329793) (39274849) (38803) (6323) (26161) (565057) (5233) ( 140453) (139537) (46817) (7300801) (37633)
3 2 437, (2) (7) (11) (19) (23) (43) (181) (439) (571) (653) (1321) _c189_2 ( 38803) (273349327681) (6323) (26161) (5233) (489061) (37441)
3 2 441, (2) (3) (5) (7) (11) (13) (19) (23) (43) (181) (439) (571) (1109) (1321) _c173_2 (1305137) (273349327681) (6661777) (14653) (99901) (2221) (7993) (1777) ( 489061) (37441)
6 2 445, (2) (3) (5) (7) (13) (31) (41) (71) (97) (223) (337) (607) (1109) (1567) _c170_3 (1305137) (12065089) (4417729) (6661777) (14653) (99901) (2221) (7993) (1777) (3079) (29569) (2521)
6 2 449, (2) (7) (31) (41) (71) (97) (223) (227) (337) (607) (677) (1567) _c184_2 (22147) (24859) (12065089) (4417729) (2939) (135601) (3079) (3389) (29569) ( 2521)
3 453, (2) (3) (5) (7) (13) (113) (151) (193) (227) (229) (457) (569) (677) _c170_4 (22147) (6269) (24859) (24730249) (18405321661) (191861) (2939) ( 135601) (2828113) (110771) (381673) (3389)
3 457, (2) (3) (5) (7) (11) (13) (19) (47) (113) (151) (181) (193) (229) (277) (457 ) (569) _c142_4 (6269) (15621601) (24730249) (4244329) (18405321661) (191861) (56857) (2828113) (110771) (1542841) (34155001) (3037) (88321) (5521) (381673 ) (2069)
4 461, (2) (7) (11) (19) (47) (59) (97) (181) (277) (349) (463) (521) _c164_2 ( 15621601) (138907099) (4244329) (2609) (56857) (1542841) (136417) (139201) ( 6961) (4177) (34155001) (3037) (88321) (5521) (2069)
4 2 2 465, (2) (3) (5) (7) (13) (17) (37) (53) (59) (73) (97) (157) (233) (313) ( 349) (463) (521) (937) _c148_2 (161149) (1327481) (138907099) (2609) (6811741 ) (5449393) (66457) (2131) (173629) (136417) (139201) (6961) (4177) (3691) ( 29017) (20593) (1873)
3 2 2 469, (2) (3) (5) (7) (13) (17) (37) (53) (73) (157) (233) (313) (353) (937) _c176_2 (161149) (1327481) (6811741) (5449393) (66457) (2131) (31153) (5783) (73751) (173629) (3691) (29017) (20593) (1873)
3 473, (2) (7) (41) (67) (71) (101) (239) (353) (443) (509) _c217_2 (31891) ( 1321442641) (31153) (5783) (73751) (4523) (2521)
5 2 477, (2) (3) (5) (7) (11) (13) (19) (29) (31) (41) (61) (67) (71) (79) (97) (101 ) (181) (193) (239) (241) (443) (509) (607) (661) (1201) _c169_4 (31891) ( 710110879) (1185361) (1321442641) (28042561) (4523) (37441) (37633) (2521) ( 20161)
5 2 481, (2) (3) (5) (7) (11) (13) (19) (23) (29) (31) (43) (61) (79) (97) (181) (193) (241) (571) (607) (661) (1201) _c182_2 (710110879) (1185361) (5081) ( 5111225857) (28042561) (489061) (37441) (37633) (20161)
3 485, (2) (7) (23) (43) (487) (571) (733) (1097) _c222_2 (986737) (250709) ( 23057) (5081) (5111225857) (3539) (489061)
3 489, (2) (3) (5) (7) (13) (83) (163) (487) (733) (1097) _c226_2 (71800513) ( 986737) (250709) (367033) (23057) (3539) (1721)
4 493, (2) (3) (5) (7) (13) (83) (97) (163) (373) _c221_2 (71800513) (37139) ( 21324529) (367033) (203857) (8059) (1721) (2543) (735073)
4 497, (2) (7) (11) (19) (97) (181) (251) (373) (499) (1049) _c203_2 (136751) ( 37139) (105251) (21324529) (274757858101) (524899) (203857) (8059) (3499) ( 2543) (735073)

> for j to 10 do d := nthdenom(a, 4*j-1); m := (3*d^2)*(1/4)+1; print(4*j-1, d, m, ifactor(m, easy)) end do;

3, 4, 13, (13)
7, 56, 2353, (13) (181)
11, 780, 456301, (181) (2521)
15, 10864, 88519873, (13) (37) (73) (2521)
19, 151316, 17172398893, (13) (37) (73) (489061)
23, 2107560, 3331356865201, (6811741) (489061)
27, 29354524, 646266059449933, (13) (61) (181) (661) (6811741)
31, 408855776, 125372284176421633, (13) (61) (181) (661) (1321442641)
35, 5694626340, 24321576864166346701, (18405321661) (1321442641)
39, 79315912984, 4718260539364094838193, (13) (757) (18405321661) (10333) (2521)

> for j from 10 to 250 do d := nthdenom(a, 4*j-1); m := (3*d^2)*(1/4)+1; print(4*j-1, ifactor(m, easy)) end do;

39, (13) (757) (18405321661) (10333) (2521)
43, (13) (277) (757) (4244329) (10333) (3037) (2521)
47, (181) (277) (274757858101) (4244329) (3037)
51, (13) (37) (73) (109) (181) (1297) (274757858101) (139537)
55, (13) (37) (73) (109) (349) (1297) (3971200609) (6961) (139537)
59, (349) (373) _c25_3 (6961)
63, (13) (373) (360250962984637) (150217) (1959673) (489061)
67, (13) (181) (57128490881281) (150217) (1959673) (489061) (2521)
71, (181) _c26_1 (99901) (2221) (2521)
2 75, (13) (157) (1636367605501) (161149) (6811741) (173629) (99901) (2221)
2 79, (13) (157) (191904140022876817) (161149) (367033) (6811741) (173629)
83, _c42_1 (367033)
87, (13) (37) (61) (73) (181) (661) _c24_1 (5199301) (10255501)
91, (13) (37) (61) (73) (181) (661) (1693) (112413322648675246168837) (5199301) (10255501)
95, (1693) _c42_2 (197569) (2521)
99, (13) (409) (613) _c19_3 (8623081) (1321442641) (994093) (197569) (2521)
103, (13) (409) (613) (7219029104975160489230437) (8623081) (1321442641) ( 994093) (71233)
107, (181) (1321) _c45_3 (71233) (489061)
111, (13) (181) (229) (457) (1321) _c28_1 (24730249) (18405321661) (489061)
115, (13) (229) (457) _c37_3 (24730249) (18405321661) (31153)
119, (733) _c61_5 (31153)
123, (13) (37) (73) (733) (757) _c32_1 (14046709069) (1122157) (10333) (24697) (2521)
127, (13) (37) (73) (181) (757) (3045046274679316654761356161) (14046709069) ( 1122157) (6811741) (10333) (24697) (2521)
131, (181) _c55_5 (28867621) (6811741) (3217)
135, (13) (277) (829) (1657) _c27_1 (10397197) (4244329) (28867621) (3217) ( 12697) (86526553) (3037)
139, (13) (277) (829) (853) (1657) (9279150820712990890957) (15349270753) ( 10397197) (4244329) (83497) (12697) (86526553) (3037)
143, (853) _c64_7 (15349270753) (83497)
147, (13) (61) (181) (601) (661) _c42_3 (300945014701) (417389101) (274757858101)
151, (13) (61) (181) (601) (661) _c25_4 (300945014701) (417389101) (274757858\ 101) (1962577) (489061) (3697) (2521)
155, _c70_3 (1962577) (489061) (3697) (2521)
159, (13) (37) (73) (109) (1297) _c66_1 (122149) (75169) (139537)
163, (13) (37) (73) (109) (1297) _c58_1 (1206157) (45817) (122149) (75169) ( 139537)
167, (181) _c69_1 (1206157) (1321442641) (45817) (19381)
171, (13) (181) (349) _c59_5 (43744993) (1321442641) (38977) (6961) (1741) (19381)
175, (13) (349) _c66_2 (43744993) (689929) (149521) (38977) (6961) (1741)
179, _c81_1 (689929) (149521) (6811741) (2521)
183, (13) (373) _c73_3 (11029373085361) (48733) (6811741) (2521)
187, (13) (181) (373) _c70_4 (11029373085361) (18405321661) (48733) (2281)
191, (181) _c84_3 (2145279937) (18405321661) (2281)
195, (13) (37) (73) (397) _c72_1 (2145279937) (1166617) (150217) (1959673) ( 489061)
199, (13) (37) (73) (397) (1213) _c80_1 (1166617) (150217) (1959673) (489061)
203, (1213) (1237) _c110_3
207, (13) (61) (181) (421) (661) (757) (1237) _c91_5 (10333) (4621) (2521)
211, (13) (61) (181) (421) (661) (757) _c88_1 (96220393) (10333) (4621) (2521)
215, _c111_1 (96220393) (5233)
219, (13) _c98_3 (5233) (6661777) (14653) (99901) (2221) (1777)
223, (13) _c99_3 (135601) (6661777) (14653) (99901) (2221) (1777)
227, (181) (277) _c97_1 (4244329) (135601) (34155001) (3037) (88321)
2 231, (13) (37) (73) (157) (181) (277) _c80_2 (161149) (4244329) (6811741) ( 173629) (34155001) (3037) (88321)
235, 2 (13) (37) (73) (157) _c97_2 (161149) (1321442641) (6811741) (173629) (2521)
239, _c118_1 (1321442641) (489061) (2521)
243, (13) _c119_1 (71800513) (367033) (489061)
247, (13) (181) _c113_1 (71800513) (274757858101) (367033)
251, (181) _c113_2 (274757858101) (11108437) (530353) (3049)
255, (13) (1549) _c111_2 (589411321) (11108437) (530353) (3049) (100621)
259, (13) (1549) _c124_1 (589411321) (407149) (100621)
263, _c123_3 (18405321661) (407149) (60667153) (2521)
267, (13) (37) (61) (73) (109) (181) (541) (661) (1297) _c71_1 (13266228061) ( 53867701) (18405321661) (5199301) (10255501) (60667153) (139537) (2521) (6481 )
271, (13) (37) (61) (73) (109) (181) (541) (661) (1297) _c91_6 (13266228061) ( 53867701) (14797) (5199301) (10255501) (139537) (6481)
275, _c153_1 (14797)
279, (13) (1693) _c148_3 (7221457)
283, (13) (1693) _c133_1 (7221457) (6811741) (489061) (44617)
287, (181) (349) _c131_5 (15115381) (6811741) (6961) (489061) (44617)
291, (13) (181) (349) (757) _c134_3 (15115381) (6961) (10333) (197569) (2521)
295, (13) (757) _c152_3 (10333) (197569) (2521)
299, _c171_3
303, (13) (37) (73) (409) (613) _c136_1 (8623081) (1321442641) (994093) (86293)
307, (13) (37) (73) (181) (373) (409) (613) _c134_4 (8623081) (1321442641) ( 994093) (86293)
311, (181) (373) _c164_3 (163909) (7537)
315, (13) _c165_1 (163909) (7537) (71233)
319, (13) (277) _c160_1 (4244329) (71233) (3037) (2521)
323, (277) _c169_5 (4244329) (3037) (2521)
327, (13) (61) (181) (661) (1321) _c159_1 (150217) (1959673) (489061)
331, (13) (61) (181) (661) (1321) _c138_3 (102541463563969) (150217) (1959673) (14029) (36073) (489061)
335, _c159_2 (102541463563969) (14029) (36073) (6811741) (2029)
339, (13) (37) (73) (229) (457) _c156_5 (24730249) (18405321661) (6811741) (2029)
343, (13) (37) (73) (229) (457) _c164_4 (24730249) (18405321661) (37369)
347, (181) _c177_1 (274757858101) (37369) (2521)
351, (13) (181) (709) _c164_5 (74990702977) (274757858101) (31153) (2521)
355, (13) (709) _c184_3 (74990702977) (31153)
359, _c205_1
363, (13) (733) _c204_1
367, (13) (181) (733) _c191_1 (99901) (2221) (6661)
371, (181) _c177_2 (522853) (1321442641) (99901) (2221) (6661) (489061)
375, (13) (37) (73) (109) (757) (1297) _c127_1 (14046709069) (703458757) ( 522853) (1321442641) (1122157) (178745617) (10333) (139537) (489061) (9829) (24697 ) (2521)
379, (13) (37) (73) (109) (757) (1297) _c150_1 (14046709069) (703458757) ( 1122157) (178745617) (10333) (139537) (9829) (24697) (2521)
383, _c219_1
2 387, (13) (61) (157) (181) (661) _c182_3 (161149) (1775281) (6811741) (173629) (19501)
2 391, (13) (61) (157) (181) (661) _c175_3 (161149) (1775281) (1264741) (4729) (6811741 ) (173629) (19501)
395, _c216_1 (1264741) (4729)
399, (13) _c210_1 (28867621) (1476949) (3217)
403, (13) (349) _c202_1 (28867621) (1476949) (3217) (6961) (2521)
407, (181) (349) _c215_1 (367033) (6961) (2521)
411, (13) (37) (73) (181) (277) (829) (1657) _c171_4 (522469) (10397197) ( 4244329) (367033) (12697) (86526553) (3037) (11593) (21529)
415, (13) (37) (73) (277) (829) (1657) _c165_2 (522469) (10397197) (4244329) ( 18405321661) (12697) (86526553) (3037) (11593) (21529) (489061)
419, _c224_1 (18405321661) (489061)
423, (13) (853) _c205_2 (15349270753) (1525933) (29146069) (83497) (4261)
427, (13) (181) (853) _c205_3 (15349270753) (1525933) (29146069) (83497) (4261)
431, (181) (373) _c238_1 (2521)
435, (13) (373) (877) _c239_1 (2521)
439, (13) (877) _c231_1 (1321442641) (6811741)
443, _c237_1 (1321442641) (6811741)
447, (13) (37) (61) (73) (181) (601) (661) _c193_1 (300945014701) (417389101) (274757858101 ) (5199301) (10255501) (1801)
451, (13) (37) (61) (73) (181) (601) (661) _c195_3 (300945014701) (417389101) (274757858101 ) (5199301) (10255501) (1801)
455, _c260_1
459, (13) (757) _c204_2 (150217) (1959673) (1962577) (146917) (10333) (489061) (312313) (388081) (3697) (9241) (2521)
463, (13) (757) _c206_1 (150217) (1959673) (1962577) (146917) (10333) (489061) (312313) (388081) (3697) (9241) (2521)
467, (181) (1693) _c252_1 (8461) (228421)
471, (13) (181) (1693) _c250_1 (3793) (8461) (228421)
475, (13) _c262_1 (54493) (3793)
479, _c269_1 (54493)
483, (13) (37) (73) (109) (1297) _c234_1 (1491013009) (122149) (75169) (139537) (33049) (2917)
487, (13) (37) (73) (109) (181) (1297) _c225_1 (1491013009) (122149) (75169) ( 139537) (33049) (197569) (2521) (2917)
491, (181) _c253_1 (18405321661) (6811741) (197569) (2521)
495, (13) (997) _c247_1 (18405321661) (1206157) (6811741) (45817) (11953)
499, (13) (997) _c266_1 (1206157) (45817) (11953)