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A294138 Number of compositions (ordered partitions) of n into proper divisors of n. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 16:03 EDT 2021. Contains 346291 sequences. (Running on oeis4.)