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A088737
Number of semiprime divisors of n-th composite number.
2
1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 1, 1, 2, 3, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 4, 1, 2, 1, 1, 3, 2, 1, 3, 3, 1, 2, 2, 1, 3, 2, 1, 1, 4, 1, 1, 1, 2, 4, 1, 2, 1, 1, 1, 2, 2, 2, 3, 3, 2, 3, 1, 3, 3, 1, 2, 3, 1, 2, 2, 1, 1, 4, 1, 1, 1, 2, 1, 4, 1, 1, 3, 4, 1, 1, 2
OFFSET
1,6
LINKS
FORMULA
a(n) = A056170(n) + A001221(n)*(A001221(n)-1)/2.
MAPLE
f:= proc(n) local p, t;
p:= numtheory:-factorset(n);
t:= nops(p);
t*(t-1)/2 + nops(select(m-> n mod m^2=0, p))
end proc:
map(f, remove(isprime, [$4..200])); # Robert Israel, May 21 2020
MATHEMATICA
a[n_] := Count[FactorInteger[n], {_, k_ /; k>1}]+PrimeNu[n](PrimeNu[n]-1)/2;
a /@ Select[Range[200], CompositeQ] (* Jean-François Alcover, Jun 22 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 12 2003
STATUS
approved