A331927 Number of compositions (ordered partitions) of n into distinct divisors of n.

1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 31, 1, 25, 1, 1, 1, 895, 1, 1, 1, 121, 1, 151, 1, 1, 1, 1, 1, 1135, 1, 1, 1, 865, 1, 31, 1, 1, 1, 1, 1, 11935, 1, 1, 1, 1, 1, 151, 1, 841, 1, 1, 1, 129439, 1, 1, 1, 1, 1, 127, 1, 1, 1, 1

Offset

0,7

Links

Table of n, a(n) for n=0..70.

Index entries for sequences related to compositions

Formula

a(n) = A331928(n) + 1 for n > 0.

Example

a(6) = 7 because we have [6], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 3, 2] and [1, 2, 3].

Prog

(PARI) a(n)={if(n==0, 1, my(v=divisors(n)); subst(serlaplace(polcoef(prod(i=1, #v, 1 + y*x^v[i] + O(x*x^n)), n)), y, 1))} \\ Andrew Howroyd, Feb 01 2020

Crossrefs

Cf. A018818, A027750, A033630, A065205, A100346, A210442, A211111, A294138, A331928.

Sequence in context: A170824 A248909 A140213 * A285483 A284097 A091258

Adjacent sequences: A331924 A331925 A331926 * A331928 A331929 A331930

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 01 2020

Status

approved