cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A106405 Number of odd semiprimes dividing n.

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%I A106405 #13 Jun 30 2022 05:57:33
%S A106405 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 A106405 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 A106405 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 A106405 Number of odd semiprimes dividing n.
%H A106405 Harvey P. Dale, <a href="/A106405/b106405.txt">Table of n, a(n) for n = 1..1000</a>
%F A106405 a(n) = A086971(n) - A106404(n);
%F A106405 a(A046315(n)) = 1; a(A093641(n)) = 0; a(A105441(n)) > 0.
%e A106405 a(105) = #{15, 21, 35} = #{3*5, 3*7, 5*7} = 3.
%t A106405 Table[Count[Divisors[n],_?(OddQ[#]&&PrimeOmega[#]==2&)],{n,120}] (* _Harvey P. Dale_, May 05 2015 *)
%t A106405 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 A106405 Cf. A000005, A001227, A046315, A086971, A093641, A105441, A106404.
%K A106405 nonn
%O A106405 1,45
%A A106405 _Reinhard Zumkeller_, May 02 2005