A278929 Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^3)).

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 1, 0, 1, 0, 0, 5, 0, 0, 3, 0, 1, 0, 0, 6, 0, 0, 6, 0, 1, 0, 0, 7, 0, 0, 10, 0, 1, 1, 0, 8, 0, 0, 15, 0, 1, 4, 0, 9, 0, 0, 21

Offset: 0

Author

Ilya Gutkovskiy, Dec 24 2016

Keywords

• nonn

Comments

Number of compositions (ordered partitions) of n into cubes of primes (A030078).

Examples

			a(35) = 2 because we have [8, 27] and [27, 8].
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A023358, A023360, A030078, A279760.

Programs

Maple

N:= 200:
Primes:= select(isprime, [2,seq(i,i=3..floor(N^(1/3)),2)]):
G:= 1/(1- add(x^(Primes[i]^3),i=1..nops(Primes))):
S:= series(G,x,N+1):
seq(coeff(S,x,j),j=0..N); # Robert Israel, Jan 23 2019

Mathematica

nmax = 120; CoefficientList[Series[1/(1 - Sum[x^Prime[k]^3, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(prime(k)^3)).