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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jun 22 2020 *)

CROSSREFS

Cf. A088738, A002808, A001358.

Sequence in context: A307848 A255326 A085424 * A318434 A321455 A096309

Adjacent sequences:  A088734 A088735 A088736 * A088738 A088739 A088740

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 12 2003

STATUS

approved

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Last modified March 8 08:16 EST 2021. Contains 341942 sequences. (Running on oeis4.)