

A280125


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


2



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
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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 partitioncounting 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 * A280586 A112344 A294080
Adjacent sequences: A280122 A280123 A280124 * A280126 A280127 A280128


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Dec 26 2016


STATUS

approved



