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A278929 Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^3)). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,36

COMMENTS

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

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of cubes

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

Cf. A023358, A023360, A030078, A279760.

Sequence in context: A066032 A035187 A291147 * A277143 A239434 A033770

Adjacent sequences:  A278926 A278927 A278928 * A278930 A278931 A278932

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 24 2016

STATUS

approved

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Last modified August 9 13:57 EDT 2020. Contains 336323 sequences. (Running on oeis4.)