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

Author

T. D. Noe, Jan 19 2011

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Programs

Mathematica

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