A281477 Expansion of Sum_{k>=1} x^(prime(k)^2)/(1 + x^(prime(k)^2)) * Product_{k>=1} (1 + x^(prime(k)^2)).

0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,13

Comments

Total number of parts in all partitions of n into distinct squares of primes (A001248).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Ilya Gutkovskiy, Extended graphical example

Index entries for related partition-counting sequences

Formula

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

Example

a(38) = 3 because we have [25, 9, 4].

Maple

Primes:= select(isprime, [$1..20]):
g:= add(x^(p^2)/(1+x^(p^2)), p=Primes)*mul(1+x^(p^2), p=Primes):
S:= series(g, x, 20^2+1):
seq(coeff(S, x, n), n=1..20^2); # Robert Israel, Feb 08 2017

Mathematica

nmax = 125; Rest[CoefficientList[Series[Sum[x^Prime[k]^2/(1 + x^Prime[k]^2), {k, 1, nmax}] Product[1 + x^Prime[k]^2, {k, 1, nmax}], {x, 0, nmax}], x]]

Crossrefs

Cf. A001248, A024938, A048261, A111900, A121518, A281449, A281542, A281668.

Sequence in context: A328959 A086080 A369054 * A070139 A116860 A179391

Adjacent sequences: A281474 A281475 A281476 * A281478 A281479 A281480

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 27 2017

Status

approved