A302354 Expansion of (Sum_{i>=1} x^prime(i))*(Sum_{j>=0} x^(j^3)).

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, 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, 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

Offset: 1

Author

Ilya Gutkovskiy, Apr 06 2018

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

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

Formula

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