A294282 -id:A294282 - cp's OEIS frontend

A294297 Integers with precisely five partitions into sums of four squares of nonnegative numbers.

50, 52, 54, 58, 70, 73, 74, 75, 76, 84, 85, 86, 89, 91, 93, 101, 103, 109, 111, 113, 127, 131, 140, 142, 143, 151, 167, 191, 200, 208, 216, 232, 280, 296, 304, 336, 344, 560, 568, 800, 832, 864, 928, 1120, 1184, 1216, 1344, 1376, 2240, 2272, 3200, 3328, 3456

Offset: 1

Robert Price, Oct 27 2017

nonn

A002635(a(n)) = 5.

Robert Price, Table of n, a(n) for n = 1..81
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No.8, October 1948, pp. 476-481.
Index entries for sequences related to sums of squares

Cf. A001156, A002635, A006431, A025428, A180149, A245022, A294282.

f[n_] := Length@ PowersRepresentations[n, 4, 2]; Select[ Range@ 3500, f@# == 5 &] (* Robert G. Wilson v, Oct 27 2017 *)

A293175 Integers with precisely six partitions into sums of four squares of nonnegative numbers.

Original entry on oeis.org

66, 81, 97, 99, 105, 110, 115, 121, 123, 124, 137, 139, 141, 149, 155, 156, 158, 159, 164, 179, 188, 239, 264, 284, 440, 496, 624, 632, 656, 752, 1056, 1136, 1760, 1984, 2496, 2528, 2624, 3008, 4224, 4544, 7040, 7936, 9984, 10112, 10496, 12032, 16896, 18176

Offset: 1

Robert Price, Oct 27 2017

nonn

A002635(a(n)) = 6.

D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
Index entries for sequences related to sums of squares

Cf. A001156, A002635, A006431, A025428, A180149, A245022, A294282, A294297.

f[n_] := Length@ PowersRepresentations[n, 4, 2]; Select[ Range@ 19000, f@# == 6 &] (* Robert G. Wilson v, Oct 27 2017 *)

A294308 Integers with precisely seven partitions into sums of four squares of nonnegative numbers.

Original entry on oeis.org

82, 98, 100, 102, 106, 108, 118, 125, 129, 132, 133, 134, 135, 161, 163, 173, 183, 197, 199, 204, 211, 212, 215, 236, 263, 328, 392, 400, 408, 424, 432, 472, 528, 536, 816, 848, 944, 1312, 1568, 1600, 1632, 1696, 1728, 1888, 2112, 2144, 3264, 3392, 3776

Offset: 1

Robert Price, Oct 27 2017

nonn

A002635(a(n)) = 7.

Robert Price, Table of n, a(n) for n = 1..74
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
Index entries for sequences related to sums of squares

Cf. A001156, A002635, A006431, A025428, A180149, A245022, A294282, A294297, A293175.

f[n_]:=Length@PowersRepresentations[n, 4, 2]; Select[Range@650, f@#==7 &] (* Vincenzo Librandi, Oct 28 2017 *)

A294310 Integers with precisely nine partitions into sums of four squares of nonnegative numbers.

Original entry on oeis.org

90, 146, 166, 174, 185, 187, 205, 206, 207, 209, 219, 220, 221, 223, 231, 235, 251, 260, 271, 287, 316, 359, 360, 380, 584, 664, 696, 824, 880, 1040, 1264, 1440, 1520, 2336, 2656, 2784, 3296, 3520, 4160, 5056, 5760, 6080, 9344, 10624, 11136, 13184, 14080

Offset: 1

Robert Price, Oct 27 2017

nonn

A002635(a(n)) = 9.

Robert Price, Table of n, a(n) for n = 1..60
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
Index entries for sequences related to sums of squares

Cf. A001156, A002635, A006431, A025428, A180149, A245022, A294282, A294297.

f[n_]:=Length@PowersRepresentations[n, 4, 2]; Select[Range@850, f@#==9 &] (* Vincenzo Librandi, Oct 28 2017 *)

A085625 Numbers that are the sum of 2 squares in exactly 2 ways.

Original entry on oeis.org

25, 50, 65, 85, 100, 125, 130, 145, 169, 170, 185, 200, 205, 221, 225, 250, 260, 265, 289, 290, 305, 338, 340, 365, 370, 377, 400, 410, 442, 445, 450, 481, 485, 493, 500, 505, 520, 530, 533, 545, 565, 578, 580, 585, 610, 629, 676, 680, 685, 689, 697, 730

Offset: 1

Hugo Pfoertner, Jul 09 2003

nonn

Wells erroneously writes that this sequence begins as 50, 65, 85, 145, ... . - Stefano Spezia, Sep 07 2024

			a(3) = 65 because 65 = 8^2 + 1^2 = 7^2 + 4^2;
a(4) = 85 because 85 = 9^2 + 2^2 = 7^2 + 6^2.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 125.

Robert Price, Table of n, a(n) for n = 1..16794

Cf. A000161, A000446, A224443, A294282, A295153, A295489, A295748.

Select[Range[730], Length[PowersRepresentations[#,2,2]]==2 &] (* Stefano Spezia, Sep 07 2024 *)

n such that A000161(n) = 2.

A294309 Integers with precisely eight partitions into sums of four squares of nonnegative numbers.

Original entry on oeis.org

114, 117, 122, 126, 145, 147, 148, 157, 165, 169, 172, 175, 177, 181, 190, 193, 203, 227, 233, 311, 456, 488, 504, 592, 688, 760, 1824, 1952, 2016, 2368, 2752, 3040, 7296, 7808, 8064, 9472, 11008, 12160, 29184, 31232, 32256, 37888, 44032, 48640

Offset: 1

Robert Price, Oct 27 2017

nonn

A002635(a(n)) = 8.

D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
Index entries for sequences related to sums of squares

Cf. A001156, A002635, A006431, A025428, A180149, A245022, A294282, A294297.

f[n_]:=Length@PowersRepresentations[n, 4, 2]; Select[Range@850, f@#==8 &] (* Vincenzo Librandi, Oct 28 2017 *)

A294311 Integers with precisely ten partitions into sums of four squares of nonnegative numbers.

Original entry on oeis.org

130, 138, 153, 154, 171, 180, 182, 195, 196, 201, 213, 214, 217, 228, 229, 238, 241, 244, 247, 249, 253, 254, 257, 259, 269, 276, 277, 281, 295, 299, 303, 308, 317, 319, 332, 335, 347, 428, 431, 520, 552, 616, 720, 728, 784, 856, 912, 952, 976, 1016, 1104

Offset: 1

Robert Price, Oct 27 2017

nonn

A002635(a(n)) = 10.

Robert Price, Table of n, a(n) for n = 1..98
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
Index entries for sequences related to sums of squares

Cf. A001156, A002635, A006431, A025428, A180149, A245022, A294282, A294297, A293175, A294308, A294309, A294310.

f[n_]:=Length@PowersRepresentations[n, 4, 2]; Select[Range@850, f@#==10 &] (* Vincenzo Librandi, Oct 28 2017 *)

cp's OEIS Frontend

A294297 Integers with precisely five partitions into sums of four squares of nonnegative numbers.

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A293175 Integers with precisely six partitions into sums of four squares of nonnegative numbers.

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A294308 Integers with precisely seven partitions into sums of four squares of nonnegative numbers.

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A294310 Integers with precisely nine partitions into sums of four squares of nonnegative numbers.

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A085625 Numbers that are the sum of 2 squares in exactly 2 ways.

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A294309 Integers with precisely eight partitions into sums of four squares of nonnegative numbers.

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A294311 Integers with precisely ten partitions into sums of four squares of nonnegative numbers.

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