A300703 Number of compositions (ordered partitions) of n into prime parts that do not divide n.

1, 0, 0, 0, 0, 2, 0, 5, 2, 5, 2, 19, 2, 45, 6, 10, 14, 231, 4, 500, 14, 48, 45, 2351, 12, 1520, 144, 637, 100, 24441, 6, 53242, 810, 2558, 1294, 15402, 94, 550862, 3707, 16658, 680, 2616337, 53, 5701552, 11639, 6606, 30749, 27077004, 800, 21212965, 5215, 611097, 109818, 280237216

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to compositions

Example

a(9) = 5 because we have [7, 2], [5, 2, 2], [2, 7], [2, 5, 2] and [2, 2, 5].

Maple

a:= proc(m) option remember; local b; b:= proc(n) option
      remember; `if`(n=0, 1, add(`if`(not isprime(j) or
       irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Mar 11 2018

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimeQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 53}]

Crossrefs

Cf. A000040, A023360, A128515, A209402, A284463, A300702, A300704, A300706.

Sequence in context: A066283 A267213 A261805 * A300706 A351481 A014842

Adjacent sequences: A300700 A300701 A300702 * A300704 A300705 A300706

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 11 2018

Status

approved