cp's OEIS Frontend

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

%I A300704 #9 Mar 16 2018 08:28:59
%S A300704 1,0,0,0,0,2,0,7,2,7,5,46,2,115,20,39,16,723,16,1819,27,559,414,11481,
%T A300704 16,13204,1763,6450,383,181548,172,455646,1326,70476,29809,571110,275,
%U A300704 7203906,121535,739513,1703,45380391,7362,113898438,65049,757426,2009203,717490902,2304
%N A300704 Number of compositions (ordered partitions) of n into prime power parts (not including 1) that do not divide n.
%H A300704 Alois P. Heinz, <a href="/A300704/b300704.txt">Table of n, a(n) for n = 0..1000</a>
%H A300704 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A300704 a(10) = 5 because we have [7, 3], [4, 3, 3], [3, 7], [3, 4, 3] and [3, 3, 4].
%p A300704 a:= proc(m) option remember; local b; b:= proc(n) option
%p A300704       remember; `if`(n=0, 1, add(`if`(nops(ifactors(j)[2])
%p A300704        <>1 or irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
%p A300704     end:
%p A300704 seq(a(n), n=0..70);  # _Alois P. Heinz_, Mar 11 2018
%t A300704 Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 48}]
%Y A300704 Cf. A246655, A280195, A284465, A300580, A300584, A300702, A300703, A300706.
%K A300704 nonn
%O A300704 0,6
%A A300704 _Ilya Gutkovskiy_, Mar 11 2018