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%I #19 Nov 26 2017 19:15:48
%S 0,4,9,17,20,30,29,38,36,45,52,53,54,65,74,68,83,77,90,84,86,99,100,
%T 107,101,108,110,117,129,116,131,125,126,146,152,140,134,192,156,149,
%U 161
%N Smallest number with exactly n representations as a sum of six nonnegative squares.
%C It appears that a(n) does not exist for n in {42, 55, 61, 74, 99, 100, 103, 125, 135, 139, 148, 152, 161, 162, 164, 168, 180, 182, 194, 196}; 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.
%t Table[SelectFirst[Range@ 200, Length@ PowersRepresentations[#, 6, 2] == n &] - Boole[n == 1], {n, 41}] (* _Michael De Vlieger_, Nov 26 2017 *)
%Y Cf. A000177, A295159.
%K nonn
%O 0,2
%A _Robert Price_, Nov 22 2017
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