A295155 Numbers that have exactly seven representations as a sum of five nonnegative squares.

50, 54, 62, 64, 65, 69, 72, 78, 87

Offset

1,1

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 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..9.

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: A081646 A215908 A052261 * A118146 A349210 A114504

Adjacent sequences: A295152 A295153 A295154 * A295156 A295157 A295158

Keyword

nonn,fini,full

Author

Robert Price, Nov 15 2017

Status

approved