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A295154 Numbers that have exactly six representations as a sum of five nonnegative squares. 0
37, 43, 45, 49, 51, 56, 63, 71, 96 (list; graph; refs; listen; history; text; internal format)
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: A176926 A217411 A155849 * A224319 A282111 A110563

Adjacent sequences:  A295151 A295152 A295153 * A295155 A295156 A295157

KEYWORD

nonn,fini,full

AUTHOR

Robert Price, Nov 15 2017

STATUS

approved

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Last modified June 17 04:45 EDT 2021. Contains 345080 sequences. (Running on oeis4.)