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A295484 Numbers that have exactly one representation as a sum of six nonnegative squares. 0
0, 1, 2, 3, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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..5.

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: A094469 A015766 A201363 * A117024 A263501 A203143

Adjacent sequences:  A295481 A295482 A295483 * A295485 A295486 A295487

KEYWORD

nonn,fini,full

AUTHOR

Robert Price, Nov 22 2017

STATUS

approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)