A280125 Expansion of Product_{k>=1} 1/((1 - x^(prime(k)^2))*(1 - x^(prime(k)^3))).

1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 3, 2, 1, 0, 3, 2, 1, 0, 4, 4, 2, 2, 4, 4, 2, 2, 5, 6, 4, 4, 7, 6, 4, 4, 8, 8, 6, 7, 10, 10, 6, 7, 11, 13, 9, 10, 15, 15, 12, 10, 16, 18, 16, 14, 20, 22, 19, 17, 21, 25, 23, 22, 26, 29, 28, 25, 30, 32, 33, 31, 37, 38, 38, 37

Offset

0,9

Comments

Number of partitions of n into parts that are squares of primes (A001248) or cubes of primes (A030078).

Links

Table of n, a(n) for n=0..79.

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/((1 - x^(prime(k)^2))*(1 - x^(prime(k)^3))).

Example

a(16) = 3 because we have [8, 8], [8, 4, 4] and [4, 4, 4, 4].

Mathematica

nmax = 100; CoefficientList[Series[Product[1/((1 - x^Prime[k]^2) (1 - x^Prime[k]^3)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000607, A001248, A023893, A030078, A090677, A111901, A131799, A168363, A279760, A280126.

Sequence in context: A168313 A072575 A025872 * A339060 A280586 A112344

Adjacent sequences: A280122 A280123 A280124 * A280126 A280127 A280128

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2016

Status

approved