A294138 Number of compositions (ordered partitions) of n into proper divisors of n.

1, 0, 1, 1, 5, 1, 24, 1, 55, 19, 128, 1, 1627, 1, 741, 449, 5271, 1, 45315, 1, 83343, 3320, 29966, 1, 5105721, 571, 200389, 26425, 5469758, 1, 154004510, 1, 47350055, 226019, 9262156, 51885, 15140335649, 1, 63346597, 2044894, 14700095925, 1, 185493291000, 1, 35539518745, 478164162

Offset: 0

Author

Ilya Gutkovskiy, Oct 23 2017

Keywords

• nonn

Examples

			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].
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..3359
• Index entries for sequences related to compositions

Crossrefs

Cf. A027750, A032741, A065205, A100346, A210442, A294137.

Programs

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}]

Formula

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

a(n) = A100346(n) - 1.