A295157 Numbers that have exactly nine representations as a sum of five nonnegative squares.

61, 67, 68, 70, 75, 76, 84, 88, 89, 92, 120

Offset: 1

Author

Robert Price, Nov 15 2017

Keywords

• nonn
• fini
• full

Comments

This sequence is finite and complete. See the von Eitzen Link. For positive integer n, if n > 6501 then the number of ways to write n as a sum of 5 squares is at least 10. So for n > 6501, there are more than eight ways to write n as a sum of 5 squares. For n <= 6501, 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

• 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.