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%I #21 Dec 02 2023 19:54:47
%S 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,
%T 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,
%U 1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,1
%N Number of prime factors (with multiplicity) of the number of distinct prime factors of n; a(n) = Omega(omega(n)).
%C 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.
%C 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
%H G. C. Greubel, <a href="/A244063/b244063.txt">Table of n, a(n) for n = 2..5000</a>
%F a(n) = A001222(A001221(n)).
%F a(n) << log log n. - _Charles R Greathouse IV_, Sep 14 2015
%t Table[PrimeOmega[PrimeNu[n]], {n, 2, 100}]
%o (PARI) a(n)=bigomega(omega(n)) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Cf. A143731, A001221 (omega), A001222 (Omega).
%K nonn
%O 2
%A _Wesley Ivan Hurt_, Jun 15 2014
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