

A280683


Number of ways to write n as an ordered sum of two positive squarefree semiprimes (A006881).


2



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 2, 2, 0, 2, 3, 2, 1, 2, 4, 0, 0, 2, 6, 2, 0, 2, 4, 4, 1, 4, 5, 4, 0, 4, 8, 6, 2, 0, 5, 4, 4, 4, 6, 4, 0, 4, 8, 10, 0, 2, 4, 6, 3, 6, 9, 4, 3, 6, 14, 8, 2, 4, 5, 8, 3, 10, 8, 4, 0, 8, 12, 4, 4, 4, 8, 6, 8, 12, 11, 6, 2, 10, 12, 12, 4, 8, 12, 12, 5, 12, 10, 4, 6
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OFFSET

1,16


COMMENTS

Conjecture: a(n) > 0 for n > 82 (see comment in A006881 from Richard R. Forberg).


LINKS

Table of n, a(n) for n=1..106.
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Semiprime
Eric Weisstein's World of Mathematics, Squarefree


FORMULA

G.f.: (Sum_{k>=2} mu(k)^2*floor(bigomega(k)/2)*floor(2/bigomega(k))*x^k)^2, where mu(k) is the Moebius function (A008683) and bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).


EXAMPLE

a(20) = 3 because we have [14, 6], [10, 10] and [6, 14].


MATHEMATICA

nmax = 106; Rest[CoefficientList[Series[(Sum[MoebiusMu[k]^2 Floor[PrimeOmega[k]/2] Floor[2/PrimeOmega[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]]


CROSSREFS

Cf. A001222, A001358, A005117, A006881, A008683, A073610, A098235, A199331.
Sequence in context: A123391 A212172 A275812 * A171871 A076260 A245527
Adjacent sequences: A280680 A280681 A280682 * A280684 A280685 A280686


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Jan 07 2017


STATUS

approved



