Search: id:a079275
|
|
A079275
|
|
Number of divisors of n that are semiprimes with distinct factors.
|
|
+0
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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(n) = omega(n)*(omega(n)-1)/2, where omega(n) is the number of distinct prime factors of n.
|
|
MAPLE
|
local a, d ;
a := 0 ;
for d in numtheory[divisors](n) do
a := a+1 ;
end if;
end do:
a ;
end proc:
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
Search completed in 0.006 seconds
|