A088737 Number of semiprime divisors of n-th composite number.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A088738, A002808, A001358.

Sequence in context: A368978 A255326 A085424 * A318434 A321455 A096309

Adjacent sequences: A088734 A088735 A088736 * A088738 A088739 A088740

Keyword

nonn

Author

Reinhard Zumkeller, Oct 12 2003

Status

approved