A280126 Expansion of Product_{k>=1} (1 + x^(prime(k)^2))*(1 + x^(prime(k)^3)).

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

Offset

0,62

Comments

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

Links

Table of n, a(n) for n=0..97.

Index entries for related partition-counting sequences

Formula

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

Example

a(61) = 2 because we have [49, 8, 4] and [25, 27, 9].

Mathematica

nmax = 120; CoefficientList[Series[Product[(1 + x^Prime[k]^2) (1 + x^Prime[k]^3), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000586, A001248, A030078, A106244, A111900, A111902, A131799, A168363, A280125.

Sequence in context: A082596 A296139 A321763 * A178536 A360001 A286656

Adjacent sequences: A280123 A280124 A280125 * A280127 A280128 A280129

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2016

Status

approved