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A285796 Number of ways to write n as an ordered sum of two numbers that are the product of an even number of distinct primes (including 1). 2

%I

%S 0,0,1,0,0,0,0,2,0,0,0,2,1,0,0,2,4,0,0,0,3,2,2,2,2,2,0,4,3,2,1,2,4,0,

%T 2,4,8,2,0,4,6,4,1,4,5,4,0,6,8,6,2,0,7,4,4,4,8,4,2,6,8,10,0,4,4,6,5,6,

%U 9,4,5,6,14,8,2,6,5,8,5,10,8,4,0,10,12,4,6,6,10,6,8,12,13,6,4,12,14,12,4,8,12

%N Number of ways to write n as an ordered sum of two numbers that are the product of an even number of distinct primes (including 1).

%C Conjecture: a(n) > 0 for all n > 82.

%F G.f.: (Sum_{k>=1} x^A030229(k))^2.

%e a(16) = 4 because we have [15, 1], [10, 6], [6, 10] and [1, 15].

%t nmax = 100; CoefficientList[Series[(Sum[Boole[MoebiusMu[k] == 1] x^k, {k, 1, nmax}])^2, {x, 0, nmax}], x]

%Y Сf. A005117, A030229, A098235, A285797.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Apr 26 2017

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Last modified October 19 20:05 EDT 2018. Contains 316378 sequences. (Running on oeis4.)