A294137 Number of compositions (ordered partitions) of n into nontrivial divisors of n.

1, 0, 0, 0, 1, 0, 2, 0, 5, 1, 2, 0, 50, 0, 2, 2, 55, 0, 185, 0, 243, 2, 2, 0, 8903, 1, 2, 19, 1219, 0, 48824, 0, 5271, 2, 2, 2, 1323569, 0, 2, 2, 369182, 0, 1659512, 0, 36636, 5111, 2, 0, 254187394, 1, 53535, 2, 223502, 0, 65005979, 2, 16774462, 2, 2, 0, 235105418684, 0, 2, 41386, 47350055, 2

Offset: 0

Author

Ilya Gutkovskiy, Oct 23 2017

Keywords

• nonn

Examples

			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].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A027750, A070824, A100346, A293813, A293814, A294138.

Programs

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}]

Formula

a(n) = [x^n] 1/(1 - Sum_{d|n, 1 < d < n} x^d).