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A295749 Numbers that have exactly eight representations of a sum of seven nonnegative squares. 0
29, 30, 33 (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 two more 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..3.

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. A025422, A295491.

Sequence in context: A165850 A129287 A007642 * A022399 A042694 A042696

Adjacent sequences:  A295746 A295747 A295748 * A295750 A295751 A295752

KEYWORD

nonn,fini,full

AUTHOR

Robert Price, Nov 26 2017

STATUS

approved

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Last modified July 28 12:14 EDT 2021. Contains 346328 sequences. (Running on oeis4.)