A106405 Number of odd semiprimes dividing n.

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, May 02 2005

Keywords

• nonn

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

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

Formula

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

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