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A281477 Expansion of Sum_{k>=1} x^(prime(k)^2)/(1 + x^(prime(k)^2)) * Product_{k>=1} (1 + x^(prime(k)^2)). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A071164 A027345 A086080 * A070139 A116860 A179391

Adjacent sequences:  A281474 A281475 A281476 * A281478 A281479 A281480

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 27 2017

STATUS

approved

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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.