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

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 3, 1, 2, 1, 2, 3, 1, 2, 4, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 1, 2, 3, 4, 1, 1, 1, 1, 3, 1, 2, 3, 1, 1, 1, 3, 1

Offset

1,27

Comments

By Lagrange's four square theorem, the minimal number of squares required to represent a number is 4 or less. See A141490 for the numbers k that have n minimal representations.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

27 has the following representations as the sum of 4 or fewer squares: 1+1+25, 9+9+9, and 1+1+9+16. The minimal number of squares is 3 and there are 2 such representations.  Hence a(27)=2.

Mathematica

Table[r=PowersRepresentations[n, 4, 2]; Sort[Tally[4-Count[#, 0]& /@ r]][[1, 2]], {n, 100}]

Crossrefs

Sequence in context: A139434 A113925 A328231 * A105083 A191770 A120966

Adjacent sequences: A180463 A180464 A180465 * A180467 A180468 A180469

Keyword

nonn

Author

T. D. Noe, Jan 19 2011

Status

approved