A244063 Number of prime factors (with multiplicity) of the number of distinct prime factors of n; a(n) = Omega(omega(n)).

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, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1

Offset

2

Comments

This sequence is not the same as A143731 and first departs from it when n = 210. The characteristic function A143731(210)=1, while a(210)=2. This is because 210 is the smallest number with 4 distinct prime factors (210 = 2*3*5*7) and 4 is the smallest composite number. Thus, Omega(omega(210)) = Omega(4) = 2.

The records for this sequence are at 2, 6, 210, 9699690, 32589158477190044730, ..., the products of the first 2^n primes. - Charles R Greathouse IV, Sep 14 2015

Links

G. C. Greubel, Table of n, a(n) for n = 2..5000

Formula

a(n) = A001222(A001221(n)).

a(n) << log log n. - Charles R Greathouse IV, Sep 14 2015

Mathematica

Table[PrimeOmega[PrimeNu[n]], {n, 2, 100}]

Prog

(PARI) a(n)=bigomega(omega(n)) \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A143731, A001221 (omega), A001222 (Omega).

Sequence in context: A341996 A341999 A118685 * A080343 A011664 A179831

Adjacent sequences: A244060 A244061 A244062 * A244064 A244065 A244066

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 15 2014

Status

approved