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
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
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
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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Feb 07 2003
STATUS
approved