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%I #26 Sep 03 2013 05:42:02
%S 1,2,3,4,6,7,9,10,12,15,18,33
%N All positive numbers that are not the sum of 5 nonzero squares.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp 12, Ellipses, Paris 2008.
%D E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, Theorem 2., p. 73.
%D Ivan Niven and Herbert S. Zuckerman, An Introduction to the Theory of Numbers, New York: John Wiley (1980), p. 145
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e 4 = 1^2 + 1^2 + 1^2 + 1^2 + 0^2, but the last square is 0, and hence 4 is in the sequence.
%e 5 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2, and therefore 5 is not in the sequence.
%t Select[ Range[100], Select[ PowersRepresentations[#, 5, 2], FreeQ[#, 0]& ] == {}& ] (* _Jean-François Alcover_, Sep 03 2013 *)
%Y Cf. A047700, A000534, A180968 (not the sum of 6 squares).
%K nonn,full,fini
%O 1,2
%A Arlin Anderson (starship1(AT)gmail.com)
%E Name changed. - _Wolfdieter Lang_, Mar 28 2013
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