

A295151


Numbers that have exactly three representations as a sum of five nonnegative squares.


0



13, 16, 17, 18, 19, 21, 22, 30, 31, 33, 39
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OFFSET

1,1


COMMENTS

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n  101) / 8) = 9. Since this sequence relaxes the restriction of zero squares, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.


REFERENCES

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


LINKS



CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



