A294743 Numbers that are the sum of 5 nonzero squares in exactly 9 ways.

101, 112, 115, 118, 127, 144, 159, 161, 165, 169, 180

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 > 6501 then the number of ways to write n as a sum of 5 squares is at least 10. For n <= 6501 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..11.

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 &] == 9]; Select[Range@250, fQ](* Robert G. Wilson v, Nov 17 2017 *)

Crossrefs

Cf. A025429, A025357, A294675, A294736.

Sequence in context: A279057 A284404 A267585 * A352439 A214527 A084413

Adjacent sequences: A294740 A294741 A294742 * A294744 A294745 A294746

Keyword

nonn,fini,full

Author

Robert Price, Nov 07 2017

Status

approved