

A294736


Numbers that are the sum of 5 nonzero squares in exactly 2 ways.


11



20, 38, 41, 45, 47, 48, 49, 50, 54, 55, 63, 66, 81, 105
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OFFSET

1,1


COMMENTS

Inspected values of n <= 50000.
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 two 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."  David A. Corneth, Nov 08 2017


REFERENCES

E. Grosswald, Representations of Integers as Sums of Squares. SpringerVerlag, New York, 1985, p. 86, Theorem 1.


LINKS



FORMULA



EXAMPLE

There are exactly two ways 20 is a sum of 5 nonzero squares. These are 1^2 + 1^2 + 1^2 + 1^2 + 4^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 = 20. Therefore 20 is in the sequence.


MATHEMATICA

Select[Range[200], Length[Select[PowersRepresentations[#, 5, 2], #[[1]] > 0&]] == 2&] (* JeanFrançois Alcover, Nov 06 2020 *)


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



