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

1,2

Comments

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

Links

Table of n, a(n) for n=1..49.

Eric W. Weisstein, MathWorld: Waring's Problem

Example

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).

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}]]

Crossrefs

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

Sequence in context: A042462 A042460 A042458 * A242184 A042482 A042484

Adjacent sequences: A141487 A141488 A141489 * A141491 A141492 A141493

Keyword

nonn

Author

Martin Renner, Jan 15 2011

Status

approved