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A300704 Number of compositions (ordered partitions) of n into prime power parts (not including 1) that do not divide n. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A254445 A140663 A198108 * A300702 A105394 A196767

Adjacent sequences:  A300701 A300702 A300703 * A300705 A300706 A300707

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 11 2018

STATUS

approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)