A141490 Least number k having n representations as the sum of the minimal number of squares, A002828.

1, 27, 28, 63, 103, 124, 135, 175, 207, 247, 255, 252, 327, 351, 412, 375, 511, 423, 543, 679, 540, 639, 687, 495, 567, 663, 759, 775, 847, 988, 783, 1111, 735, 1327, 855, 927, 1191, 999, 1308, 975, 1143, 1383, 1263, 1071, 1463, 1359, 1495, 1375, 1479

Offset: 1

Author

Martin Renner, Jan 15 2011

Keywords

• nonn

Comments

That is, a(n) is the least k such that A180466(k) = n.

Examples

			a(1) = 1 since 1 = 1^2;
a(2) = 27 since 27 = 1^2 + 1^2 + 5^2 = 3^2 + 3^2 + 3^2 (2 ways);
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).
		

Links

• Eric W. Weisstein, MathWorld: Waring's Problem

Crossrefs

Cf. A180466 (number of representations of n as a minimal number of squares, A002828(n))

Programs

Mathematica

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}]]