cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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

Views

Author

David W. Wilson

Keywords

Examples

			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

Links

Crossrefs

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

Programs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

A025326 Numbers that are the sum of 3 nonzero squares in exactly 6 ways.

Original entry on oeis.org

209, 297, 306, 314, 321, 326, 329, 342, 425, 426, 434, 441, 458, 459, 489, 497, 513, 530, 531, 534, 542, 546, 558, 561, 593, 602, 605, 633, 649, 650, 657, 659, 662, 665, 674, 675, 678, 681, 693, 698, 699, 705, 706, 713, 714, 725, 737, 738, 741, 746, 747, 750, 755, 758
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

A343967 Numbers that are the sum of three positive cubes in five or more ways.

Original entry on oeis.org

161568, 262683, 314712, 326808, 359568, 443197, 444536, 471960, 503208, 513729, 515376, 526023, 529199, 532683, 552824, 597960, 702729, 736371, 746992, 806688, 844416, 863379, 907479, 924048, 931419, 975213, 1011067, 1028663, 1062937, 1092853, 1152152, 1172016, 1211048, 1232496, 1258011
Offset: 1

Views

Author

David Consiglio, Jr., May 05 2021

Keywords

Examples

			314712 =  4^3 +  6^3 + 68^3
       =  5^3 + 24^3 + 67^3
       =  6^3 + 30^3 + 66^3
       = 31^3 + 41^3 + 60^3
       = 36^3 + 48^3 + 54^3
so 314712 is a term of this sequence.

Links

Crossrefs

Cf. A025333, A051167, A343968, A343970, A343987, A344364, A345083.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
for pos in cwr(power_terms,3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 5])
for x in range(len(rets)):
    print(rets[x])

A025296 Numbers that are the sum of 2 nonzero squares in 5 or more ways.

Original entry on oeis.org

5525, 8125, 8450, 9425, 10625, 11050, 12025, 12325, 13325, 14365, 14450, 15725, 16250, 17225, 17425, 18125, 18785, 18850, 19825, 21125, 21250, 22100, 22525, 23125, 23725, 24050, 24505, 24650, 25625, 25925, 26650, 26825, 27625, 28730, 28925, 29725
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025288, A025295, A025297, A025333, A051167.

Programs

  • Maple
    N:= 10^5: # generate all entries <=N
V:= Vector(N,datatype=integer[4]):
for a from 1 to floor(sqrt(N)) do
  for b from a do
    n:= a^2 + b^2;
    if n > N then break fi;
    V[n]:= V[n]+1
od od:
select(t -> V[t] >= 5, [$1..N]); # Robert Israel, Jun 01 2025
  • Mathematica
    nn = 30000; t = Table[0, {nn}]; lim = Floor[Sqrt[nn - 1]]; Do[num = i^2 + j^2; If[num <= nn, t[[num]]++], {i, lim}, {j, i}]; Flatten[Position[t, ?(# >= 5 &)]] (* _T. D. Noe, Apr 07 2011 *)

A025370 Numbers that are the sum of 4 nonzero squares in 5 or more ways.

Original entry on oeis.org

82, 90, 100, 102, 103, 106, 108, 111, 114, 115, 117, 118, 122, 124, 126, 127, 130, 132, 133, 135, 138, 143, 145, 147, 148, 150, 151, 153, 154, 156, 157, 159, 162, 163, 165, 166, 167, 169, 170, 171, 172, 174, 175, 177, 178, 180, 181, 182, 183, 186, 187, 188, 189, 190
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025333, A025361, A025369, A025371, A343987, A344798.

Formula

{n: A025428(n) >= 5}. Union of A025371 and A025361. - R. J. Mathar, Jun 15 2018
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