A295494 -id:A295494 - cp's OEIS frontend

A295669 Largest number with exactly n representations as a sum of six nonnegative squares.

7, 15, 23, 31, 32, 40, 48, 55, 64, 58, 63, 71, 79, 96, 88, 78, 85, 97, 112, 93, 106, 111, 120, 121, 128, 136, 130, 122, 160, 145, 139, 141, 151, 168, 159, 157, 169, 192, 156, 184, 178

Offset: 1

Robert Price, Nov 25 2017

It appears that a(42) does not exist.

E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.

Cf. A000177, A025430, A295494.

A295702 Largest number with exactly n representations as a sum of six positive squares.

Original entry on oeis.org

43, 64, 67, 82, 91, 106, 112, 109, 115, 133, 139, 154, 131, 160, 146, 178, 163, 181, 166, 169, 202, 187, 172, 226, 208, 211, 229, 196, 217, 232, 203, 256, 223, 274, 253

Offset: 1

Robert Price, Nov 25 2017

It appears that a(36) does not exist.

E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.

Cf. A000177, A025430, A295494, A295669.

A295752 Smallest number with exactly n representations as a sum of seven nonnegative squares.

Original entry on oeis.org

0, 4, 9, 13, 18, 21, 25, 29, 34, 36, 37, 46, 49, 50, 45, 53, 58, 54, 68, 61, 66, 74, 69, 70, 78, 77, 81, 84, 86

Offset: 0

Robert Price, Nov 26 2017

nonn

It appears that a(n) does not exist for n in {30, 35, 45, 49, 57, 63, 67, 75, 77, 78, 82, 84, 85, 97, 100, 101, 104, 110, 112, 115, 116, 119, 123, 124, 125, 134, 136, 137, 140, 142, 143, 148, 149, 150, 151, 158, 159, 160, 162, 168, 170, 172, 174, 175, 176, 180, 183, 184, 185, 187, 188, 191, 198}; i.e., there is no integer whose number of representations is any of these values.

E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.

Cf. A025422, A295494.

cp's OEIS Frontend

A295669 Largest number with exactly n representations as a sum of six nonnegative squares.

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A295702 Largest number with exactly n representations as a sum of six positive squares.

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A295752 Smallest number with exactly n representations as a sum of seven nonnegative squares.

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