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A295490 Numbers that have exactly seven representations as a sum of six nonnegative squares. 1
29, 37, 42, 43, 47, 48 (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 and allows one more square, 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..6.

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. A000177, A294524, A295150.

Sequence in context: A250291 A127956 A166088 * A172195 A161724 A046502

Adjacent sequences:  A295487 A295488 A295489 * A295491 A295492 A295493

KEYWORD

nonn,fini,full

AUTHOR

Robert Price, Nov 22 2017

STATUS

approved

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Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)