The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #5 Nov 27 2017 12:47:50
%S 0,4,9,13,18,21,25,29,34,36,37,46,49,50,45,53,58,54,68,61,66,74,69,70,
%T 78,77,81,84,86
%N Smallest number with exactly n representations as a sum of seven nonnegative squares.
%C It appears that a(n) does not exist for n in {30, 35, 45, 49, 57, 63, 67, 75, 77, 78, 82, 84, 85, 97, 100, 101, 104, 110, 112, 115, 116, 119, 123, 124, 125, 134, 136, 137, 140, 142, 143, 148, 149, 150, 151, 158, 159, 160, 162, 168, 170, 172, 174, 175, 176, 180, 183, 184, 185, 187, 188, 191, 198}; 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. A025422, A295494.
%K nonn
%O 0,2
%A _Robert Price_, Nov 26 2017