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

Links

Robert Israel, Table of n, a(n) for n = 0..250

Index entries for sequences related to compositions

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

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

Sequence in context: A132775 A174102 A217521 * A252943 A294617 A320450

Adjacent sequences: A331922 A331923 A331924 * A331926 A331927 A331928

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 01 2020

Status

approved