A295751 Numbers that have exactly ten representations as a sum of seven nonnegative squares.

36, 38, 40, 41, 43, 44, 47

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..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.

Crossrefs

Cf. A025422, A295493.

Sequence in context: A218052 A098079 A160553 * A031317 A257441 A181457

Adjacent sequences: A295748 A295749 A295750 * A295752 A295753 A295754

Keyword

nonn,fini,full

Author

Robert Price, Nov 26 2017

Status

approved