

A294675


Numbers that are the sum of 5 nonzero squares in exactly 1 way.


41



5, 8, 11, 13, 14, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 34, 36, 39, 42, 57, 60
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OFFSET

1,1


COMMENTS

The sequence is likely to be 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 one way 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. SpringerVerlag, New York, 1985, p. 86, Theorem 1.


LINKS



FORMULA



MATHEMATICA

Select[Range[100], Length[Select[PowersRepresentations[#, 5, 2], #[[1]] > 0&]] == 1&] (* JeanFrançois Alcover, Feb 25 2019 *)
b[n_, i_, k_, t_] := b[n, i, k, t] = If[n == 0, If[t == 0, 1, 0], If[i<1  t<1, 0, b[n, i  1, k, t] + If[i^2 > n, 0, b[n  i^2, i, k, t  1]]]];
T[n_, k_] := b[n, Sqrt[n] // Floor, k, k];


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



