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A180466
The number of representations of n as a minimal number of squares, A002828(n).
6
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.
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: A113925 A373248 A328231 * A105083 A372571 A191770
KEYWORD
nonn
AUTHOR
T. D. Noe, Jan 19 2011
STATUS
approved