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.

A025372 Numbers that are the sum of 4 nonzero squares in 7 or more ways.

Original entry on oeis.org

130, 135, 138, 148, 150, 154, 162, 170, 172, 175, 178, 180, 182, 183, 186, 187, 189, 190, 195, 196, 198, 199, 202, 207, 210, 213, 214, 215, 217, 218, 220, 222, 223, 225, 226, 228, 229, 230, 231, 234, 235, 237, 238, 242, 243, 244, 245, 246, 247, 250, 252, 253, 255, 258
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025335, A025363, A025371, A025373, A344800, A345150.

Programs

  • Maple
    N:= 1000: # for terms <= N
B:= Vector(N):
for i from 1 while 4*i^2 <= N do
  for j from i while i^2 + 3*j^2 <= N do
    for k from j while i^2 + j^2 + 2*k^2 <= N do
      for l from k do
        m:= i^2 + j^2 + k^2 + l^2;
        if m > N then break fi;
        B[m]:= B[m]+1
od od od od:
select(t -> B[t] >= 7, [$1..N]); # Robert Israel, Oct 23 2020

Formula

{n: A025428(n) >= 7}. - R. J. Mathar, Jun 15 2018

A345086 Numbers that are the sum of three third powers in seven or more ways.

Original entry on oeis.org

2016496, 2562624, 4525632, 4783680, 5268024, 5618250, 6366816, 6525000, 6755328, 7374375, 7451352, 7457120, 8275392, 9063144, 9086104, 9931167, 10036872, 10266138, 10371024, 10973880, 12002472, 12452049, 12742920, 12983517, 13581352, 13639816, 13641480
Offset: 1

Views

Author

David Consiglio, Jr., Jun 07 2021

Keywords

Examples

			2016496 is a term 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.

Links

Crossrefs

Cf. A025335, A344729, A345083, A345085, A345087, A345150.

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 >= 7])
for x in range(len(rets)):
    print(rets[x])

A025298 Numbers that are the sum of 2 nonzero squares in 7 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, 105625, 107185, 110500, 111605, 112625
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025290, A025297, A025299, A025335.

Programs

  • Mathematica
    Parallelize[Select[Range[120000],Length[PowersRepresentations[#,2,2]]>6&]]  (* Harvey P. Dale, Feb 19 2011 *)
nn = 112625; 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, ?(# >= 7 &)]] (* _T. D. Noe, Apr 07 2011 *)
Previous Showing 11-20 of 20 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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