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A295489 Numbers that have exactly six representations as a sum of six nonnegative squares. 1
30, 33, 34, 35, 39, 40 (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: A328737 A118616 A181456 * A344807 A095489 A095483

Adjacent sequences:  A295486 A295487 A295488 * A295490 A295491 A295492

KEYWORD

nonn,fini,full

AUTHOR

Robert Price, Nov 22 2017

STATUS

approved

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)