A106405 - OEIS

%I #13 Jun 30 2022 05:57:33

%S 0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0,

%T 1,1,0,0,1,0,0,1,0,0,2,0,0,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,2,0,1,1,0,0,

%U 1,1,0,1,0,0,2,0,1,1,0,0,1,0,0,1,1,0,1,0,0,2,1,0,1,0,1,0,0,1,2,1,0,1,0,0,3

%N Number of odd semiprimes dividing n.

%H Harvey P. Dale, <a href="/A106405/b106405.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A086971(n) - A106404(n);

%F a(A046315(n)) = 1; a(A093641(n)) = 0; a(A105441(n)) > 0.

%e a(105) = #{15, 21, 35} = #{3*5, 3*7, 5*7} = 3.

%t Table[Count[Divisors[n],_?(OddQ[#]&&PrimeOmega[#]==2&)],{n,120}] (* _Harvey P. Dale_, May 05 2015 *)

%t a[n_] := Count[e = FactorInteger[n][[;; , 2]], _?(# > 1 &)] + (o = Length[e])*(o - 1)/2 - If[EvenQ[n], If[e[[1]] > 1, o, o - 1], 0]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2022 *)

%Y Cf. A000005, A001227, A046315, A086971, A093641, A105441, A106404.

%K nonn

%O 1,45

%A _Reinhard Zumkeller_, May 02 2005