A278912 Expansion of Product_{k>=1} 1/(1 - x^prime(prime(k))).

1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 4, 3, 4, 4, 3, 5, 5, 5, 6, 5, 6, 8, 7, 8, 9, 8, 10, 11, 10, 12, 12, 13, 15, 14, 16, 17, 17, 19, 20, 20, 22, 24, 24, 26, 27, 28, 31, 31, 33, 36, 35, 39, 42, 41, 45, 47, 48, 53, 54, 55, 60, 61, 65, 69, 69, 74, 78, 80, 85, 88, 90, 96, 101, 104, 109, 113, 117, 124, 128, 133, 139

Offset: 0

Author

Ilya Gutkovskiy, Nov 30 2016

Keywords

• nonn
• easy

Comments

Number of partitions of n into primes with prime subscripts.

Examples

			a(11) = 2 because we have [3,3,5] and [11], where 3 = prime(2) = prime(prime(1)), 5 = prime(3) = prime(prime(2)) and 11 = prime(5) = prime(prime(3)).
		

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Prime Partition
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000040, A000607, A006450.

Programs

Mathematica

nmax=90; CoefficientList[Series[1/Product[1 - x^Prime[Prime[k]], {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^A006450(k)).

G.f.: Product_{k>=1} 1/(1 - x^A000040(A000040(k))).