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A295156 Numbers that have exactly eight representations as a sum of five nonnegative squares. 0
52, 53, 58, 59, 66, 73, 79, 80, 81, 95, 105 (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..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: A327374 A327109 A327108 * A181461 A050422 A226753

Adjacent sequences:  A295153 A295154 A295155 * A295157 A295158 A295159

KEYWORD

nonn,fini,full

AUTHOR

Robert Price, Nov 15 2017

STATUS

approved

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Last modified May 15 10:25 EDT 2021. Contains 343909 sequences. (Running on oeis4.)