A295158 Numbers that have exactly ten representations as a sum of five nonnegative squares.

74, 93, 97, 111

Offset

1,1

Comments

This sequence is finite and complete. See the von Eitzen Link. For positive integer n, if n > 7845 then the number of ways to write n as a sum of 5 squares is at least 11. So for n > 7845, there are more than nine ways to write n as a sum of 5 squares. For n <= 7845, it has been verified if n is in the sequence by inspection. Hence the sequence is complete.

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. A000174, A006431, A294675.

Sequence in context: A305265 A055111 A020203 * A039484 A098516 A209925

Adjacent sequences: A295155 A295156 A295157 * A295159 A295160 A295161

Keyword

nonn,fini,full

Author

Robert Price, Nov 15 2017

Status

approved