OFFSET
0,5
LINKS
FORMULA
a(n) = [x^n] 1/(1 - Sum_{d|n, d < n} x^d).
a(n) = A100346(n) - 1.
EXAMPLE
a(4) = 5 because 4 has 3 divisors {1, 2, 4} among which 2 are proper divisors {1, 2} therefore we have [2, 2], [2, 1, 1], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].
MATHEMATICA
Table[d = Divisors[n]; Coefficient[Series[1/(1 - Sum[Boole[d[[k]] != n] x^d[[k]], {k, Length[d]}]), {x, 0, n}], x, n], {n, 0, 45}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 23 2017
STATUS
approved