A285797 - OEIS

%I #4 Apr 26 2017 21:57:07

%S 0,0,0,0,1,2,1,2,2,2,3,0,2,2,3,2,4,0,4,2,4,2,5,0,6,2,5,0,4,0,6,2,6,4,

%T 7,2,8,2,3,2,6,2,8,4,8,4,7,4,10,6,8,0,6,4,10,4,6,0,7,4,13,6,5,2,10,2,

%U 12,2,6,4,10,6,16,10,9,4,10,6,14,4,10,6,9,10,17,8,9,2,8,10,18,6,8,2,9,6,16,6,6,4,14

%N Number of ways to write n as an ordered sum of two numbers that are the product of an odd number of distinct primes.

%C Conjecture: a(n) > 0 for all n > 57.

%F G.f.: (Sum_{k>=1} x^A030059(k))^2.

%e a(10) = 3 because we have [7, 3], [5, 5] and [3, 7].

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

%Y Cf. A005117, A030059, A098235, A285796.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Apr 26 2017