A079275 - OEIS

%I #25 Jan 18 2021 04:47:55

%S 0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,1,0,1,0,1,0,3,0,0,1,1,

%T 1,1,0,1,1,1,0,3,0,1,1,1,0,1,0,1,1,1,0,1,1,1,1,1,0,3,0,1,1,0,1,3,0,1,

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

%N Number of divisors of n that are semiprimes with distinct factors.

%C Number of pairs of prime factors of n, (p,q), such that p < q. For example, the prime factors of 30 are 2, 3 and 5, so we have the ordered pairs (2,3), (2,5) and (3,5). - _Wesley Ivan Hurt_, Sep 14 2020

%H G. C. Greubel, <a href="/A079275/b079275.txt">Table of n, a(n) for n = 1..1000</a>

%F a(A000961(n)) = 0; a(A007774(n)) = 1; a(A033992(n)) = 3; a(A033993(n)) = 6.

%F a(n) = omega(n)*(omega(n)-1)/2, where omega(n) is the number of distinct prime factors of n.

%F a(n) = Sum_{p|n, q|n, p,q prime, p<q} 1. - _Wesley Ivan Hurt_, Sep 14 2020

%p A079275 := proc(n)

%p     local a,d ;

%p     a := 0 ;

%p     for d in numtheory[divisors](n) do

%p         if A001221(d) = 2 and A001222(d) = 2 then

%p             a := a+1 ;

%p         end if;

%p     end do:

%p     a ;

%p end proc:

%p seq(A079275(n),n=1..40) ; # _R. J. Mathar_, Jan 18 2021

%t f[n_]:=Module[{c=PrimeNu[n]},(c(c-1))/2]; Array[f,110] (* _Harvey P. Dale_, Oct 05 2011 *)

%o (PARI) a(n) = sumdiv(n, d, (bigomega(d)==2) && (omega(d)==2)); \\ _Michel Marcus_, Sep 15 2020

%o (PARI) a(n) = binomial(omega(n),2) \\ _David A. Corneth_, Sep 15 2020

%Y Cf. A000005, A000961, A001221, A001358, A006881, A007774, A033992, A033993.

%K nonn,easy

%O 1,30

%A _Reinhard Zumkeller_, Feb 07 2003