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A283760
Expansion of (Sum_{i>=1} x^prime(i))*(Sum_{j>=1} x^(j^3)).
5
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
1,30
COMMENTS
Number of representations of n as the sum of a prime number and a positive cube.
LINKS
FORMULA
G.f.: (Sum_{i>=1} x^prime(i))*(Sum_{j>=1} x^(j^3)).
EXAMPLE
a(32) = 2 because 32 = 31 + 1^3 = 5 + 3^3.
MATHEMATICA
nmax = 120; Rest[CoefficientList[Series[Sum[x^Prime[i], {i, 1, nmax}] Sum[x^j^3, {j, 1, nmax}], {x, 0, nmax}], x]]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 16 2017
STATUS
approved