A294738 Numbers that are the sum of 5 nonzero squares in exactly 4 ways.

62, 70, 71, 72, 75, 76, 82, 84, 89, 97, 108, 129, 132

Offset

1,1

Comments

This sequence is likely finite and complete as the next term, if it exists, is > 50000.

From a proof by David A. Corneth on Nov 08 2017 in A294736: This sequence is complete, see the von Eitzen Link and Price's computation that the next term must be > 50000. Proof. The link mentions "for positive integer n, if n > 5408 then the number of ways to write n as a sum of 5 squares is at least Floor(Sqrt(n - 101) / 8)". So for n > 5408, there are more than eight ways to write n as a sum of 5 squares. For n <= 5408, it has been verified if n is in the sequence by inspection. Hence the sequence is complete.

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..13.

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.

Eric Weisstein's World of Mathematics, Square Number.

Index entries for sequences related to sums of squares

Crossrefs

Cf. A025429, A025357, A294675, A294736, A294737.

Sequence in context: A025340 A048127 A047823 * A044997 A138172 A074772

Adjacent sequences: A294735 A294736 A294737 * A294739 A294740 A294741

Keyword

nonn,fini,full

Author

Robert Price, Nov 07 2017

Status

approved