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Expansion of (Sum_{i>=1} x^prime(i))*(Sum_{j>=0} x^(j^3)).
4

%I #4 Apr 06 2018 17:28:41

%S 0,1,2,1,1,1,1,1,0,1,2,1,2,1,1,0,1,1,2,1,1,0,1,1,1,0,1,0,2,2,2,2,0,1,

%T 0,0,2,2,1,1,1,1,1,2,1,1,1,1,1,1,1,0,1,1,1,1,0,1,1,1,2,1,0,1,0,1,3,2,

%U 2,1,2,1,1,2,2,0,1,0,2,2,2,0,2,1,0,1,2,1,1,1,1,0,1,1,1,0,2,2,0,1,2,1,1,1,2,1,2,1,2,2,2,0,1,1,1,1,2

%N Expansion of (Sum_{i>=1} x^prime(i))*(Sum_{j>=0} x^(j^3)).

%C Number of representations of n as the sum of a prime number and a nonnegative cube.

%F G.f.: (Sum_{i>=1} x^prime(i))*(Sum_{j>=0} x^(j^3)).

%e a(11) = 2 because 11 = 3 + 2^3 = 11 + 0^3.

%t nmax = 120; Rest[CoefficientList[Series[Sum[x^Prime[i], {i, 1, nmax}] Sum[x^j^3, {j, 0, nmax}], {x, 0, nmax}], x]]

%Y Cf. A002471, A010051, A010057, A045911, A064272, A283760.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Apr 06 2018