

A294743


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


2



101, 112, 115, 118, 127, 144, 159, 161, 165, 169, 180
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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. SpringerVerlag, New York, 1985, p. 86, Theorem 1.


LINKS



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



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



