A047701 All positive numbers that are not the sum of 5 nonzero squares.

1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 18, 33

Offset: 1

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn
• full
• fini

Examples

			4 = 1^2 + 1^2 + 1^2 + 1^2 + 0^2, but the last square is 0, and hence 4 is in the sequence.
5 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2, and therefore 5 is not in the sequence.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp 12, Ellipses, Paris 2008.
• E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, Theorem 2., p. 73.
• Ivan Niven and Herbert S. Zuckerman, An Introduction to the Theory of Numbers, New York: John Wiley (1980), p. 145

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A047700, A000534, A180968 (not the sum of 6 squares).

Programs

Mathematica

Select[ Range[100], Select[ PowersRepresentations[#, 5, 2], FreeQ[#, 0]& ] == {}& ] (* Jean-François Alcover, Sep 03 2013 *)

Extensions

Name changed. - Wolfdieter Lang, Mar 28 2013