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A331925 Number of compositions (ordered partitions) of n into distinct prime powers (including 1).

%I A331925 #10 Jun 29 2024 09:09:29
%S A331925 1,1,1,3,3,5,10,11,17,19,48,49,62,85,120,258,175,337,464,631,646,932,
%T A331925 1686,1991,2122,2455,4118,4545,6010,6481,13302,14383,16177,16912,
%U A331925 26454,32024,35468,42389,57334,107708,73830,125629,142560,200377,172752,244624
%N A331925 Number of compositions (ordered partitions) of n into distinct prime powers (including 1).
%H A331925 Robert Israel, <a href="/A331925/b331925.txt">Table of n, a(n) for n = 0..250</a>
%H A331925 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A331925 a(6) = 10 because we have [5, 1], [4, 2], [3, 2, 1], [3, 1, 2], [2, 4], [2, 3, 1], [2, 1, 3], [1, 5], [1, 3, 2] and [1, 2, 3].
%p A331925 N:= 50: # for a(0)..a(N)
%p A331925 P:= select(isprime, [2,seq(i,i=3..N,2)]):
%p A331925 PP:= sort([1,seq(seq(p^j, j = 1 .. ilog[p](N)),p=P)]):G:= 1:
%p A331925 for s in PP do
%p A331925   G:= G + series(G*x*y^s,y,N+1);
%p A331925 od:
%p A331925 G:= convert(G,polynom):
%p A331925 T:= add(coeff(G,x,i)*i!,i=0..N):
%p A331925 seq(coeff(T,y,i),i=0..N); # _Robert Israel_, Jun 28 2024
%Y A331925 Cf. A000961, A023893, A106244, A219107, A280543, A331847.
%K A331925 nonn
%O A331925 0,4
%A A331925 _Ilya Gutkovskiy_, Feb 01 2020