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A079275
Number of divisors of n that are semiprimes with distinct factors.
13
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, 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, 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
OFFSET
1,30
COMMENTS
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
LINKS
FORMULA
a(A000961(n)) = 0; a(A007774(n)) = 1; a(A033992(n)) = 3; a(A033993(n)) = 6.
a(n) = omega(n)*(omega(n)-1)/2, where omega(n) is the number of distinct prime factors of n.
a(n) = Sum_{p|n, q|n, p,q prime, p<q} 1. - Wesley Ivan Hurt, Sep 14 2020
MAPLE
A079275 := proc(n)
local a, d ;
a := 0 ;
for d in numtheory[divisors](n) do
if A001221(d) = 2 and A001222(d) = 2 then
a := a+1 ;
end if;
end do:
a ;
end proc:
seq(A079275(n), n=1..40) ; # R. J. Mathar, Jan 18 2021
MATHEMATICA
f[n_]:=Module[{c=PrimeNu[n]}, (c(c-1))/2]; Array[f, 110] (* Harvey P. Dale, Oct 05 2011 *)
PROG
(PARI) a(n) = sumdiv(n, d, (bigomega(d)==2) && (omega(d)==2)); \\ Michel Marcus, Sep 15 2020
(PARI) a(n) = binomial(omega(n), 2) \\ David A. Corneth, Sep 15 2020
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Feb 07 2003
STATUS
approved