OFFSET
1,2
COMMENTS
Total number of parts in all compositions (ordered partitions) of n into squarefree parts (A005117).
FORMULA
G.f.: Sum_{i>=1} mu(i)^2*x^i / (1 - Sum_{j>=1} mu(j)^2*x^j)^2.
EXAMPLE
a(4) = 19 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2], [1, 1, 1, 1] and 2 + 2 + 3 + 2 + 3 + 3 + 4 = 19.
MATHEMATICA
nmax = 36; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i, {i, 1, nmax}]/(1 - Sum[MoebiusMu[j]^2 x^j, {j, 1, nmax}])^2, {x, 0, nmax}], x]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 30 2017
STATUS
approved