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

0,5

Links

Amiram Eldar, Table of n, a(n) for n = 0..3359

Index entries for sequences related to compositions

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

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

Sequence in context: A147476 A146675 A201884 * A207824 A179900 A123967

Adjacent sequences: A294135 A294136 A294137 * A294139 A294140 A294141

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 23 2017

Status

approved