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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A025334 Numbers that are the sum of 3 nonzero squares in 6 or more ways.

Original entry on oeis.org

209, 297, 306, 314, 321, 326, 329, 341, 342, 369, 374, 425, 426, 434, 441, 446, 458, 459, 461, 486, 489, 494, 497, 506, 509, 513, 521, 530, 531, 534, 542, 545, 546, 549, 558, 561, 566, 569, 581, 593, 594, 602, 605, 614, 621, 626, 629, 633, 641, 649, 650, 654, 657, 659
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025297, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025371, A025427, A345083.

A025335 Numbers that are the sum of 3 nonzero squares in 7 or more ways.

Original entry on oeis.org

341, 369, 374, 446, 461, 486, 494, 506, 509, 521, 545, 549, 566, 569, 581, 594, 614, 621, 626, 629, 641, 654, 666, 677, 686, 689, 701, 710, 726, 729, 731, 734, 749, 761, 770, 774, 789, 794, 797, 801, 806, 809, 810, 818, 821, 825, 833, 846, 849, 854, 857, 866, 869, 881
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025298, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025372, A025427, A345086.

A025336 Numbers that are the sum of 3 nonzero squares in 8 or more ways.

Original entry on oeis.org

374, 446, 486, 521, 566, 569, 594, 614, 621, 626, 629, 686, 689, 701, 710, 729, 734, 749, 761, 770, 774, 789, 794, 801, 809, 810, 825, 846, 849, 854, 857, 866, 869, 881, 902, 909, 914, 926, 929, 941, 945, 950, 953, 965, 969, 971, 974, 986, 989, 990, 1001, 1014, 1022
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025299, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025373, A025427, A345087.

A025337 Numbers that are the sum of 3 nonzero squares in 9 or more ways.

Original entry on oeis.org

594, 614, 626, 689, 734, 761, 774, 794, 801, 846, 854, 866, 881, 909, 914, 926, 929, 941, 950, 965, 974, 986, 989, 990, 1001, 1025, 1026, 1034, 1041, 1046, 1049, 1062, 1070, 1074, 1089, 1091, 1097, 1106, 1109, 1118, 1121, 1130, 1134, 1139, 1154, 1161, 1166
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025300, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025374, A025427, A345119.

A025338 Numbers that are the sum of 3 nonzero squares in 10 or more ways.

Original entry on oeis.org

594, 734, 761, 794, 801, 846, 854, 866, 881, 909, 926, 941, 950, 965, 986, 1001, 1026, 1034, 1041, 1046, 1049, 1089, 1106, 1109, 1121, 1130, 1154, 1161, 1169, 1181, 1190, 1206, 1209, 1214, 1226, 1238, 1265, 1274, 1286, 1301, 1314, 1322, 1326, 1329, 1341
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025301, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025375, A025427, A345121.

A004214 Positive numbers that are not the sum of three nonzero squares.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 13, 15, 16, 20, 23, 25, 28, 31, 32, 37, 39, 40, 47, 52, 55, 58, 60, 63, 64, 71, 79, 80, 85, 87, 92, 95, 100, 103, 111, 112, 119, 124, 127, 128, 130, 135, 143, 148, 151, 156, 159, 160, 167, 175, 183, 188, 191, 199, 207, 208, 215, 220, 223, 231
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Not of the form x^2 + y^2 + z^2 with x, y, z >= 1.
Complement of A000408, but skipping the zero. - R. J. Mathar, Nov 23 2006
A025427(a(n)) = 0. - Reinhard Zumkeller, Feb 26 2015

Examples

			The smallest numbers that are the sums of 3 nonzero squares are 3=1+1+1, 6=1+1+4, 9=1+4+4, etc.

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A000408, A025427.

Programs

  • Haskell
    a004214 n = a004214_list !! (n-1)
a004214_list = filter ((== 0) . a025427) [1..]
-- Reinhard Zumkeller, Feb 26 2015
  • Maple
    gf := sum(sum(sum(q^(x^2+y^2+z^2), x=1..25), y=1..25), z=1..25): s := series(gf, q, 500): for n from 1 to 500 do if coeff(s, q, n)=0 then printf(`%d,`,n) fi:od:
  • Mathematica
    f[n_] := Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, n}]^3, x]], n^2], 0]];f[16] (* Ray Chandler, Dec 06 2006 *)
  • PARI
    isA000408(n)={ local(a,b) ; a=1; while(a^2+1A004214(n)={ return(! isA000408(n)) ; }
n=1 ; for(an=1,20000, if(isA004214(an), print(n," ",an); n++)) \\ R. J. Mathar, Nov 23 2006

Extensions

More terms from James Sellers, Apr 20 2001
Name clarified by Wolfdieter Lang, Apr 04 2013

A025331 Numbers that are the sum of 3 nonzero squares in 3 or more ways.

Original entry on oeis.org

54, 66, 81, 86, 89, 99, 101, 110, 114, 126, 129, 131, 134, 146, 149, 150, 153, 161, 162, 166, 171, 173, 174, 179, 182, 185, 186, 189, 194, 198, 201, 206, 209, 216, 219, 221, 222, 225, 227, 230, 233, 234, 237, 241, 242, 243, 245, 246, 249, 251, 254, 257, 258, 261, 264
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025294, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025368, A025398, A025427.

A025322 Numbers that are the sum of 3 nonzero squares in exactly 2 ways.

Original entry on oeis.org

27, 33, 38, 41, 51, 57, 59, 62, 69, 74, 75, 77, 83, 90, 94, 98, 102, 105, 107, 108, 113, 117, 118, 121, 122, 123, 125, 132, 137, 138, 139, 141, 147, 152, 154, 155, 158, 164, 165, 170, 177, 178, 181, 187, 195, 197, 203, 204, 210, 211, 213, 214, 217, 218, 226, 228, 229, 236
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.

Programs

  • Mathematica
    okQ[n_]:=Length[Select[PowersRepresentations[n,3,2],!MemberQ[ #,0]&]] ==2; Select[Range[250],okQ] (* Harvey P. Dale, Jul 25 2011 *)

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

Original entry on oeis.org

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

Views

Author

David W. Wilson

Keywords

Examples

			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

Links

Crossrefs

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

Programs

Formula

{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

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

Previous Showing 11-20 of 37 results. Next

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