OFFSET
0,7
FORMULA
a(n) = [x^n] 1/(1 - Sum_{d|n, 1 < d < n} x^d).
EXAMPLE
a(8) = 5 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are nontrivial divisors {2, 4} therefore we have [4, 4], [4, 2, 2], [2, 4, 2], [2, 2, 4] and [2, 2, 2, 2].
MATHEMATICA
Table[d = Divisors[n]; Coefficient[Series[1/(1 - Sum[Boole[d[[k]] != 1 && d[[k]] != n] x^d[[k]], {k, Length[d]}]), {x, 0, n}], x, n], {n, 0, 65}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 23 2017
STATUS
approved