A280715 Expansion of Product_{k>=1} 1/((1 - x^prime(k))*(1 - x^(prime(k)^2))*(1 - x^(prime(k)^3))).

1, 0, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 15, 19, 23, 29, 36, 44, 53, 65, 78, 94, 112, 134, 159, 189, 222, 263, 307, 361, 420, 491, 569, 661, 764, 883, 1017, 1170, 1343, 1539, 1761, 2011, 2293, 2611, 2968, 3369, 3819, 4323, 4887, 5518, 6222, 7007, 7883, 8857, 9942, 11144, 12483, 13964, 15609, 17426, 19440, 21664

Offset

0,5

Comments

Number of partitions of n into parts that are primes (A000040), squares of primes (A001248) or cubes of primes (A030078).

Links

Table of n, a(n) for n=0..61.

Index entries for related partition-counting sequences

Formula

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

Example

a(8) = 6 because we have [8], [5, 3], [4, 4], [4, 2, 2], [3, 3, 2], [2, 2, 2, 2].

Mathematica

nmax = 61; CoefficientList[Series[Product[1/((1 - x^Prime[k]) (1 - x^Prime[k]^2) (1 - x^Prime[k]^3)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000040, A000607, A001248, A023893, A030078, A087797, A090677, A111901, A279760, A280125.

Sequence in context: A266747 A246762 A093950 * A023894 A285799 A241772

Adjacent sequences: A280712 A280713 A280714 * A280716 A280717 A280718

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 07 2017

Status

approved