cp's OEIS Frontend

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

%I A300703 #9 Mar 16 2018 05:52:31
%S A300703 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,
%T A300703 1520,144,637,100,24441,6,53242,810,2558,1294,15402,94,550862,3707,
%U A300703 16658,680,2616337,53,5701552,11639,6606,30749,27077004,800,21212965,5215,611097,109818,280237216
%N A300703 Number of compositions (ordered partitions) of n into prime parts that do not divide n.
%H A300703 Alois P. Heinz, <a href="/A300703/b300703.txt">Table of n, a(n) for n = 0..1000</a>
%H A300703 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A300703 a(9) = 5 because we have [7, 2], [5, 2, 2], [2, 7], [2, 5, 2] and [2, 2, 5].
%p A300703 a:= proc(m) option remember; local b; b:= proc(n) option
%p A300703       remember; `if`(n=0, 1, add(`if`(not isprime(j) or
%p A300703        irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
%p A300703     end:
%p A300703 seq(a(n), n=0..80);  # _Alois P. Heinz_, Mar 11 2018
%t A300703 Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimeQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 53}]
%Y A300703 Cf. A000040, A023360, A128515, A209402, A284463, A300702, A300704, A300706.
%K A300703 nonn
%O A300703 0,6
%A A300703 _Ilya Gutkovskiy_, Mar 11 2018