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A295488 Numbers that have exactly five representations as a sum of six nonnegative squares. 1
20, 21, 25, 26, 27, 28, 32 (list; graph; refs; listen; history; text; internal format)



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.


E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.


Table of n, a(n) for n=1..7.

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.


Cf. A000177, A294524, A295150.

Sequence in context: A138601 A278582 A218539 * A008940 A014368 A118865

Adjacent sequences:  A295485 A295486 A295487 * A295489 A295490 A295491




Robert Price, Nov 22 2017



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Last modified May 24 01:29 EDT 2019. Contains 323528 sequences. (Running on oeis4.)