A025326 -id:A025326 - cp's OEIS frontend

A025323 Numbers that are the sum of 3 nonzero squares in exactly 3 ways.

54, 66, 81, 86, 89, 99, 101, 110, 114, 126, 131, 149, 150, 162, 166, 173, 174, 179, 182, 185, 186, 216, 219, 221, 222, 225, 227, 233, 237, 241, 242, 245, 258, 264, 274, 275, 286, 291, 302, 305, 309, 315, 318, 323, 324, 334, 338, 344, 347, 349, 356, 361, 366, 377, 396

Offset: 1

David W. Wilson

nonn

			182 is a term because 182 = 1^2 + 9^2 + 10^2 = 2^2 + 3^2 + 13^2 = 5^2 + 6^2 + 11^2 and there are no more such sums of three nonzero squares giving 182. - _David A. Corneth_, Feb 13 2019

David A. Corneth, Table of n, a(n) for n = 1..1069 (first 418 terms from Robert Price, terms < 2*10^6)
David A. Corneth, PARI program
David A. Corneth, Terms below (inclusive) 2*10^6 with the sums of squares
Eric Weisstein's World of Mathematics, Square Number.
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

Select[Range@ 400, Length@ # == 3 &@ DeleteCases[PowersRepresentations[#, 3, 2], ?(AnyTrue[#, # == 0 &] &)] &] (* _Michael De Vlieger, Feb 13 2019 *)

\\ See Corneth link. David A. Corneth, Feb 13 2019

{n: A025427(n) = 3}. - R. J. Mathar, Aug 05 2022

A025324 Numbers that are the sum of 3 nonzero squares in exactly 4 ways.

Original entry on oeis.org

129, 134, 146, 153, 161, 171, 189, 198, 201, 234, 243, 246, 249, 251, 254, 257, 261, 270, 278, 285, 290, 293, 294, 299, 339, 353, 362, 363, 365, 371, 378, 387, 390, 393, 395, 405, 406, 409, 411, 417, 429, 451, 454, 465, 467, 469, 473, 477, 485, 501, 502, 510, 514, 516

Offset: 1

David W. Wilson

nonn

			299 is a term because 299 = 1^2 + 3^2 + 17^2 = 3^2 + 11^2 + 13^2 = 5^2 + 7^2 + 15^2 = 7^2 + 9^2 + 13^2 and there are no more such sums of four nonzero squares giving 182. - _David A. Corneth_, Feb 13 2019

David A. Corneth, Table of n, a(n) for n = 1..1705 (first 593 terms from Robert Price, terms <= 2*10^6)
David A. Corneth, Terms below (inclusive) 2*10^6 with the sums of squares
David A. Corneth, PARI program
Eric Weisstein's World of Mathematics, Square Number.
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

Select[Range@ 600, Length@ # == 4 &@ DeleteCases[PowersRepresentations[#, 3, 2], ?(AnyTrue[#, # == 0 &] &)] &] (* _Michael De Vlieger, Feb 13 2019 *)

\\ See Corneth link \\ David A. Corneth, Feb 13 2019

A025325 Numbers that are the sum of 3 nonzero squares in exactly 5 ways.

Original entry on oeis.org

194, 206, 230, 266, 269, 281, 350, 354, 381, 386, 389, 398, 401, 402, 413, 414, 419, 437, 449, 450, 470, 474, 482, 491, 525, 539, 554, 563, 579, 582, 585, 590, 601, 611, 630, 635, 638, 642, 646, 722, 769, 776, 781, 786, 819, 824, 829, 830, 834, 851, 867, 874, 878, 886

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..441
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025327 Numbers that are the sum of 3 nonzero squares in exactly 7 ways.

Original entry on oeis.org

341, 369, 461, 494, 506, 509, 545, 549, 581, 641, 654, 666, 677, 726, 731, 797, 806, 818, 821, 833, 882, 891, 893, 894, 899, 906, 934, 954, 978, 981, 998, 1011, 1017, 1019, 1050, 1067, 1069, 1086, 1094, 1098, 1101, 1133, 1158, 1194, 1211, 1233, 1294, 1331, 1346

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..422
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025328 Numbers that are the sum of 3 nonzero squares in exactly 8 ways.

Original entry on oeis.org

374, 446, 486, 521, 566, 569, 621, 629, 686, 701, 710, 729, 749, 770, 789, 809, 810, 825, 849, 857, 869, 902, 945, 953, 969, 971, 1014, 1022, 1029, 1053, 1085, 1125, 1146, 1174, 1217, 1221, 1241, 1242, 1245, 1249, 1250, 1253, 1254, 1259, 1269, 1277, 1334, 1379

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..649
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025329 Numbers that are the sum of 3 nonzero squares in exactly 9 ways.

Original entry on oeis.org

614, 626, 689, 774, 914, 929, 974, 989, 990, 1025, 1062, 1070, 1074, 1091, 1097, 1118, 1134, 1139, 1166, 1179, 1193, 1205, 1229, 1251, 1262, 1266, 1289, 1298, 1305, 1310, 1325, 1409, 1433, 1446, 1470, 1541, 1571, 1611, 1637, 1638, 1745, 1754, 1821, 1834

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..400
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025330 Numbers that are the sum of 3 nonzero squares in exactly 10 ways.

Original entry on oeis.org

594, 734, 761, 794, 801, 846, 881, 909, 926, 965, 986, 1001, 1026, 1041, 1089, 1130, 1190, 1209, 1214, 1226, 1265, 1274, 1322, 1326, 1329, 1341, 1370, 1382, 1386, 1505, 1509, 1553, 1557, 1581, 1586, 1613, 1625, 1658, 1689, 1691, 1709, 1713, 1725, 1739

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..592
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A345084 Numbers that are the sum of three third powers in exactly six ways.

Original entry on oeis.org

1296378, 1371735, 1409400, 1614185, 1824040, 1885248, 2101464, 2302028, 2305395, 2542968, 2851848, 2889216, 2974392, 2988441, 3185792, 3380833, 3681280, 3689496, 3706984, 3775680, 3906657, 4109832, 4123008, 4142683, 4422592, 4842872, 4952312, 5005125, 5023656

Offset: 1

David Consiglio, Jr., Jun 07 2021

nonn

Differs from A345083 at term 7 because 2016496 = 5^3 + 71^3 + 117^3 = 9^3 + 65^3 + 119^3 = 18^3 + 20^3 + 125^3 = 46^3 + 96^3 + 99^3 = 53^3 + 59^3 + 117^3 = 65^3 + 89^3 + 99^3 = 82^3 + 84^3 + 93^3.

			1296378 is a term because 1296378 = 3^3 + 75^3 + 94^3  = 8^3 + 32^3 + 107^3  = 20^3 + 76^3 + 93^3  = 30^3 + 58^3 + 101^3  = 32^3 + 80^3 + 89^3  = 59^3 + 74^3 + 86^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Cf. A025326, A343970, A344648, A345083, A345085, A345149.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 6])
for x in range(len(rets)):
    print(rets[x])

cp's OEIS Frontend

A025323 Numbers that are the sum of 3 nonzero squares in exactly 3 ways.

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A025324 Numbers that are the sum of 3 nonzero squares in exactly 4 ways.

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A025325 Numbers that are the sum of 3 nonzero squares in exactly 5 ways.

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A025327 Numbers that are the sum of 3 nonzero squares in exactly 7 ways.

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A025328 Numbers that are the sum of 3 nonzero squares in exactly 8 ways.

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A025329 Numbers that are the sum of 3 nonzero squares in exactly 9 ways.

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A025330 Numbers that are the sum of 3 nonzero squares in exactly 10 ways.

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A345084 Numbers that are the sum of three third powers in exactly six ways.

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