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

1,45

Links

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

Formula

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A236389 A337821 A143078 * A228601 A363856 A369354

Adjacent sequences: A106402 A106403 A106404 * A106406 A106407 A106408

Keyword

nonn

Author

Reinhard Zumkeller, May 02 2005

Status

approved