A283760 Expansion of (Sum_{i>=1} x^prime(i))*(Sum_{j>=1} x^(j^3)).

0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 2, 2, 2, 1, 1, 1, 0, 2, 2, 0, 1, 0, 1, 2, 2, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 0, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 2, 2

Offset: 1

Author

Ilya Gutkovskiy, Mar 16 2017

Keywords

• nonn

Comments

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

Examples

			a(32) = 2 because 32 = 31 + 1^3 = 5 + 3^3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Ilya Gutkovskiy, Extended graphical example

Crossrefs

Cf. A000040, A000578, A064272, A211167.

Programs

Mathematica

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

PARI

concat([0,0], Vec((sum(i=1, 120, x^prime(i)) * sum(j=1, 120, x^(j^3))) + O(x^121))) \\ Indranil Ghosh, Mar 16 2017

Scheme

(define (A283760 n) (cond ((< n 2) 0) (else (let loop ((k (A048766 n)) (s 0)) (if (< k 1) s (loop (- k 1) (+ s (A010051 (- n (expt k 3)))))))))) ;; Antti Karttunen, Aug 18 2017

Formula

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