Search: id:a079275
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A079275
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Number of divisors of n that are semiprimes with distinct factors.
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+0
13
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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
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OFFSET
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1,30
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = omega(n)*(omega(n)-1)/2, where omega(n) is the number of distinct prime factors of n.
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MAPLE
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local a, d ;
a := 0 ;
for d in numtheory[divisors](n) do
a := a+1 ;
end if;
end do:
a ;
end proc:
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MATHEMATICA
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f[n_]:=Module[{c=PrimeNu[n]}, (c(c-1))/2]; Array[f, 110] (* Harvey P. Dale, Oct 05 2011 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (bigomega(d)==2) && (omega(d)==2)); \\ Michel Marcus, Sep 15 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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