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A331925
Number of compositions (ordered partitions) of n into distinct prime powers (including 1).
1
1, 1, 1, 3, 3, 5, 10, 11, 17, 19, 48, 49, 62, 85, 120, 258, 175, 337, 464, 631, 646, 932, 1686, 1991, 2122, 2455, 4118, 4545, 6010, 6481, 13302, 14383, 16177, 16912, 26454, 32024, 35468, 42389, 57334, 107708, 73830, 125629, 142560, 200377, 172752, 244624
OFFSET
0,4
EXAMPLE
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].
MAPLE
N:= 50: # for a(0)..a(N)
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
PP:= sort([1, seq(seq(p^j, j = 1 .. ilog[p](N)), p=P)]):G:= 1:
for s in PP do
G:= G + series(G*x*y^s, y, N+1);
od:
G:= convert(G, polynom):
T:= add(coeff(G, x, i)*i!, i=0..N):
seq(coeff(T, y, i), i=0..N); # Robert Israel, Jun 28 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 01 2020
STATUS
approved