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

%I

%S 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,

%T 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,

%U 22,19,17,21,25,23,22,26,29,28,25,30,32,33,31,37,38,38,37

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

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

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

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

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

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

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

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Dec 26 2016

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Last modified August 10 22:22 EDT 2020. Contains 336403 sequences. (Running on oeis4.)