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

1,1

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

Table of n, a(n) for n=1..11.

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: A346808 A345485 A295805 * A095575 A095563 A014753

Adjacent sequences: A295154 A295155 A295156 * A295158 A295159 A295160

Keyword

nonn,fini,full

Author

Robert Price, Nov 15 2017

Status

approved