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.

Previous Showing 11-20 of 20 results.

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.

A345087 Numbers that are the sum of three third powers in eight or more ways.

Original entry on oeis.org

2562624, 5618250, 6525000, 6755328, 7374375, 12742920, 13581352, 14027112, 14288373, 14926248, 16819704, 18443160, 20168784, 20500992, 22783032, 23113728, 25305048, 26936064, 27131840, 29515968, 30205440, 32835375, 34012224, 38269440, 39317832, 39339000
Offset: 1

Views

Author

David Consiglio, Jr., Jun 07 2021

Keywords

Examples

			2562624 is a term because 2562624 = 7^3 + 35^3 + 135^3  = 7^3 + 63^3 + 131^3  = 11^3 + 99^3 + 115^3  = 16^3 + 45^3 + 134^3  = 29^3 + 102^3 + 112^3  = 35^3 + 59^3 + 131^3  = 50^3 + 84^3 + 121^3  = 68^3 + 71^3 + 122^3.

Links

Crossrefs

Cf. A025336, A344737, A345086, A345088, A345119, A345152.

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, 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 >= 8])
for x in range(len(rets)):
    print(rets[x])

A025373 Numbers that are the sum of 4 nonzero squares in 8 or more ways.

Original entry on oeis.org

130, 138, 150, 154, 162, 175, 178, 180, 186, 195, 196, 198, 202, 207, 210, 213, 214, 217, 218, 220, 222, 223, 225, 226, 228, 230, 231, 234, 235, 237, 238, 242, 243, 244, 246, 247, 250, 252, 253, 255, 258, 259, 262, 265, 266, 267, 268, 270, 271, 273, 274, 275, 276, 277
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025336, A025364, A025372, A025374, A344801, A345152.

Programs

  • Mathematica
    selQ[n_] := Length[ Select[ PowersRepresentations[n, 4, 2], Times @@ # != 0 &]] >= 8; Select[ Range[300], selQ] (* Jean-François Alcover, Oct 03 2013 *)

Formula

{n: A025428(n) >= 8}. - R. J. Mathar, Jun 15 2018

A025299 Numbers that are the sum of 2 nonzero squares in 8 or more ways.

Original entry on oeis.org

27625, 32045, 40885, 45305, 47125, 55250, 58565, 60125, 61625, 64090, 66625, 67405, 69745, 71825, 77285, 78625, 80665, 81770, 86125, 87125, 90610, 91205, 93925, 94250, 98345, 98605, 99125, 99905, 101065, 107185, 110500, 111605, 112625, 114985
Offset: 1

Views

Author

David W. Wilson

Keywords

Examples

			27625 is in the sequence via 20^2 + 165^2 = 27^2 + 164^2 = 45^2 + 160^2 = 60^2 + 155^2 = 83^2 + 144^2 = 88^2 + 141^2 = 101^2 + 132^2 = 115^2 + 120^2. - _David A. Corneth_, Jun 01 2025

Links

Crossrefs

Cf. A025291, A025298, A025300, A025336.

Programs

  • Mathematica
    nn = 114985; 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, ?(# >= 8 &)]] (* _T. D. Noe, Apr 07 2011 *)
  • PARI
    upto(n) = {my(v = vector(n)); for(i = 1, sqrtint(n), i2 = i^2; for(j = i, sqrtint(n - i^2), v[i2 + j^2]++)); select(x->x >= 8, v, 1)} \\ David A. Corneth, Jun 01 2025
Previous Showing 11-20 of 20 results.

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