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

0,7

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to compositions

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

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

Sequence in context: A350158 A327806 A319683 * A246723 A339168 A370896

Adjacent sequences: A294134 A294135 A294136 * A294138 A294139 A294140

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 23 2017

Status

approved