A300704 Number of compositions (ordered partitions) of n into prime power parts (not including 1) that do not divide n.

1, 0, 0, 0, 0, 2, 0, 7, 2, 7, 5, 46, 2, 115, 20, 39, 16, 723, 16, 1819, 27, 559, 414, 11481, 16, 13204, 1763, 6450, 383, 181548, 172, 455646, 1326, 70476, 29809, 571110, 275, 7203906, 121535, 739513, 1703, 45380391, 7362, 113898438, 65049, 757426, 2009203, 717490902, 2304

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(10) = 5 because we have [7, 3], [4, 3, 3], [3, 7], [3, 4, 3] and [3, 3, 4].

Maple

a:= proc(m) option remember; local b; b:= proc(n) option
      remember; `if`(n=0, 1, add(`if`(nops(ifactors(j)[2])
       <>1 or irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Mar 11 2018

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 48}]

Crossrefs

Cf. A246655, A280195, A284465, A300580, A300584, A300702, A300703, A300706.

Sequence in context: A346670 A140663 A198108 * A300702 A353273 A105394

Adjacent sequences: A300701 A300702 A300703 * A300705 A300706 A300707

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 11 2018

Status

approved