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%I #32 May 26 2015 04:36:42
%S 1,27,28,63,103,124,135,175,207,247,255,252,327,351,412,375,511,423,
%T 543,679,540,639,687,495,567,663,759,775,847,988,783,1111,735,1327,
%U 855,927,1191,999,1308,975,1143,1383,1263,1071,1463,1359,1495,1375,1479
%N Least number k having n representations as the sum of the minimal number of squares, A002828.
%C That is, a(n) is the least k such that A180466(k) = n.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/WaringsProblem.html">MathWorld: Waring's Problem</a>
%e a(1) = 1 since 1 = 1^2;
%e a(2) = 27 since 27 = 1^2 + 1^2 + 5^2 = 3^2 + 3^2 + 3^2 (2 ways);
%e a(3) = 28 since 28 = 1^2 + 1^2 + 1^2 +5^2 = 1^2 + 3^2 + 3^2 + 3^2 = 2^2 + 2^2 + 2^2 + 4^2 (3 ways).
%t t=Table[r=PowersRepresentations[n, 4, 2]; Sort[Tally[4-Count[#, 0] & /@ r]][[1, 2]], {n, 1000}]; u=Union[t]; c=Complement[Range[Max[u]], u]; If[c == {}, mx=u[[-1]], mx=c[[1]]-1]; Flatten[Table[Position[t, n, 1, 1], {n, mx}]]
%Y Cf. A180466 (number of representations of n as a minimal number of squares, A002828(n))
%K nonn
%O 1,2
%A _Martin Renner_, Jan 15 2011