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

1,3

Comments

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

Links

Table of n, a(n) for n=1..117.

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A267611 A178666 A206706 * A000164 A330261 A157746

Adjacent sequences: A302351 A302352 A302353 * A302355 A302356 A302357

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 06 2018

Status

approved