A294741 Numbers that are the sum of 5 nonzero squares in exactly 7 ways.

77, 83, 85, 88, 94, 99, 120, 124, 130, 137, 138, 150, 156, 201

Offset

1,1

Comments

Theorem: There are no further terms. Proof (from a proof by David A. Corneth on Nov 08 2017 in A294736): The von Eitzen link states that 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) = 9. For n <= 5408, terms have been verified by inspection. Hence this sequence is finite and 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..14.

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

Mathematica

fQ[n_] := Block[{pr = PowersRepresentations[n, 5, 2]}, Length@Select[pr, #[[1]] > 0 &] == 7]; Select[Range@250, fQ] (* Robert G. Wilson v, Nov 17 2017 *)

Crossrefs

Cf. A025429, A025357, A294675, A294736.

Sequence in context: A217545 A344799 A344800 * A052202 A089525 A274172

Adjacent sequences: A294738 A294739 A294740 * A294742 A294743 A294744

Keyword

nonn,fini,full

Author

Robert Price, Nov 07 2017

Status

approved