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A106404 Number of even semiprimes dividing n.

%I A106404 #33 Jun 26 2022 02:18:10
%S A106404 0,0,0,1,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,0,2,0,1,0,1,
%T A106404 0,2,0,1,0,2,0,2,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,3,0,1,0,1,0,2,0,2,
%U A106404 0,2,0,2,0,1,0,2,0,2,0,2,0,1,0,3,0,1,0,2,0,2,0,2,0,1,0,2,0,1,0,2,0,2,0,2,0
%N A106404 Number of even semiprimes dividing n.
%C A106404 Also the number of prime divisors p|n such that n/p is even. - _Gus Wiseman_, Jun 06 2018
%H A106404 Reinhard Zumkeller, <a href="/A106404/b106404.txt">Table of n, a(n) for n = 1..10000</a>
%F A106404 a(n) = A086971(n) - A106405(n).
%F A106404 a(A100484(n)) = 1.
%F A106404 a(A005408(n)) = 0.
%F A106404 a(A005843(n)) > 0 for n>1.
%F A106404 a(2n) = omega(n), a(2n+1) = 0, where omega(n) is the number of distinct prime divisors of n, A001221. - _Franklin T. Adams-Watters_, Jun 09 2006
%F A106404 a(n) = card { d | d*p = n, d even, p prime }. - _Peter Luschny_, Jan 30 2012
%F A106404 O.g.f.: Sum_{p prime} x^(2p)/(1 - x^(2p)). - _Gus Wiseman_, Jun 06 2018
%e A106404 a(60) = #{4, 6, 10} = #{2*2, 2*3, 2*5} = 3.
%t A106404 Table[Length[Select[Divisors[n],PrimeQ[#]&&EvenQ[n/#]&]],{n,100}] (* _Gus Wiseman_, Jun 06 2018 *)
%t A106404 Table[Count[Divisors[n],_?(EvenQ[#]&&PrimeOmega[#]==2&)],{n,110}] (* _Harvey P. Dale_, May 04 2021 *)
%t A106404 a[n_] := If[EvenQ[n], PrimeNu[n/2], 0]; Array[a, 100] (* _Amiram Eldar_, Jun 26 2022 *)
%o A106404 (Sage)
%o A106404 def A106404(n):
%o A106404     return add(1-(n/d)%2 for d in divisors(n) if is_prime(d))
%o A106404 print([A106404(n) for n in (1..105)])  # Peter Luschny, Jan 30 2012
%o A106404 (PARI) a(n)=if(n%2,0,omega(n/2)) \\ _Charles R Greathouse IV_, Jan 30 2012
%o A106404 (Haskell)
%o A106404 a106404 n = length [d | d <- takeWhile (<= n) a100484_list, mod n d == 0]
%o A106404 -- _Reinhard Zumkeller_, Jan 31 2012
%Y A106404 Cf. A000005, A000607, A001221, A001227, A008683, A083399, A088705, A100484, A205745, A305614.
%K A106404 nonn
%O A106404 1,12
%A A106404 _Reinhard Zumkeller_, May 02 2005