A286935 Number of partitions of n into primes which are the difference of two consecutive cubes (A002407).

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 2, 2

Offset: 0

Author

Ilya Gutkovskiy, May 16 2017

Keywords

• nonn

Examples

			a(56) = 2 because we have [37, 19] and [7, 7, 7, 7, 7, 7, 7, 7].
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Cuban Prime
• Eric Weisstein's World of Mathematics, Hex Number
• Index entries for sequences related to centered polygonal numbers
• Index entries for sequences related to partitions

Crossrefs

Cf. A000607, A002407, A003215, A280953, A286934.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - x^k), {k, Select[(Range[nmax] + 1)^3 - Range[nmax]^3, PrimeQ]}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^A002407(k)).