A295493 Numbers that have exactly ten representations as a sum of six nonnegative squares.

45, 50, 56, 58

Offset

1,1

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 7845, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least 11. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 7845 is at least 11. Then an inspection of n <= 7845 completes the proof.

References

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

Links

Table of n, a(n) for n=1..4.

H. von Eitzen, in reply to user James47, What is the largest integer with only one representation as a sum of five nonzero squares? on stackexchange.com, May 2014

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

Crossrefs

Cf. A000177, A294524, A295150.

Sequence in context: A045566 A274368 A214572 * A184043 A345482 A295802

Adjacent sequences: A295490 A295491 A295492 * A295494 A295495 A295496

Keyword

nonn,fini,full

Author

Robert Price, Nov 22 2017

Status

approved