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%I #6 Nov 29 2017 23:09:19
%S 0,4,8,13,16,20,22,25,30,29,34
%N Smallest number with exactly n representations as a sum of eight nonnegative squares.
%C It appears that a(n) does not exist for n in {12, 24, 39, 40, 48, 50, 53, 58, 60, 64, 67, 70, 71, 75, 78, 81, 83, 85, 86, 87, 91, 92, 96, 102, 103, 108, 113, 115, 120, 122, 123, 124, 128, 129, 130, 132, 135, 136, 138, 140, 142, 143, 144, 145, 148, 150, 151, 155, 156, 158, 160, 161, 164, 168, 170, 171, 172, 174, 175, 177, 178, 181, 183, 185, 186, 188, 189, 190, 196, 197, 198, 199, 200}; i.e., there is no integer whose number of representations is any of these values.
%D E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.
%H D. H. Lehmer, <a href="http://www.jstor.org/stable/2305380">On the Partition of Numbers into Squares</a>, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
%Y Cf. A025423, A295752.
%K nonn,more
%O 0,2
%A _Robert Price_, Nov 29 2017