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A058061 Number of prime factors (counted with multiplicity) of d(n), the number of divisors of n. 7
0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

From Bernard Schott, Mar 24 2020: (Start)

a(n) = 1 iff n = p^(q-1) with p, q primes (A009087).

a(n) = 2 if n=p*q with p, q primes (A006881), or if n=p^2*q with p, q primes (A054753), or if n=p^4*q with p, q primes (A178739), or if n=p^6*q with p, q primes (A189987), or if n=p^2*q^4 with p, q primes (A189988), or if n=p^(m-1) with p prime and m is semiprime in A001358 (not exhaustive). (End)

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001222(A000005(n)).

EXAMPLE

For n=120, d(120)=16, a(120)=4.

MATHEMATICA

Table[PrimeOmega@ DivisorSigma[0, n], {n, 120}] (* Michael De Vlieger, Feb 18 2017 *)

PROG

(PARI) a(n) = bigomega(numdiv(n)); \\ Michel Marcus, Dec 14 2013

CROSSREFS

Cf. A001222, A000005, A058060.

Sequence in context: A160980 A065031 A305832 * A064547 A318306 A214715

Adjacent sequences:  A058058 A058059 A058060 * A058062 A058063 A058064

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 23 2000

STATUS

approved

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Last modified June 20 13:53 EDT 2021. Contains 345165 sequences. (Running on oeis4.)