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A278929
Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^3)).
2
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
0,36
COMMENTS
Number of compositions (ordered partitions) of n into cubes of primes (A030078).
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^(prime(k)^3)).
EXAMPLE
a(35) = 2 because we have [8, 27] and [27, 8].
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 24 2016
STATUS
approved