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Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^3)).
2

%I #46 Jan 23 2019 20:00:24

%S 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,

%T 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,

%U 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

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

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

%H Robert Israel, <a href="/A278929/b278929.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

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

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

%p N:= 200:

%p Primes:= select(isprime, [2,seq(i,i=3..floor(N^(1/3)),2)]):

%p G:= 1/(1- add(x^(Primes[i]^3),i=1..nops(Primes))):

%p S:= series(G,x,N+1):

%p seq(coeff(S,x,j),j=0..N); # _Robert Israel_, Jan 23 2019

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

%Y Cf. A023358, A023360, A030078, A279760.

%K nonn

%O 0,36

%A _Ilya Gutkovskiy_, Dec 24 2016