A331925 - OEIS

%I #10 Jun 29 2024 09:09:29

%S 1,1,1,3,3,5,10,11,17,19,48,49,62,85,120,258,175,337,464,631,646,932,

%T 1686,1991,2122,2455,4118,4545,6010,6481,13302,14383,16177,16912,

%U 26454,32024,35468,42389,57334,107708,73830,125629,142560,200377,172752,244624

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

%H Robert Israel, <a href="/A331925/b331925.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%e 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 N:= 50: # for a(0)..a(N)

%p P:= select(isprime, [2,seq(i,i=3..N,2)]):

%p PP:= sort([1,seq(seq(p^j, j = 1 .. ilog[p](N)),p=P)]):G:= 1:

%p for s in PP do

%p   G:= G + series(G*x*y^s,y,N+1);

%p od:

%p G:= convert(G,polynom):

%p T:= add(coeff(G,x,i)*i!,i=0..N):

%p seq(coeff(T,y,i),i=0..N); # _Robert Israel_, Jun 28 2024

%Y Cf. A000961, A023893, A106244, A219107, A280543, A331847.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Feb 01 2020