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%I #21 Aug 24 2024 06:08:25
%S 0,1,2,2,2,2,2,2,2,3,2,2,3,2,2,2,3,3,3,2,3,2,3,3,2,3,3,2,3,3,3,3,3,3,
%T 3,3,2,3,3,3,3,3,2,3,3,4,3,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,3,3,
%U 3,3,3,3,3,3,3,3,4,3,3,3,4,3,2,3,3,3,3,3,4,3,3,3,3,3,2,3,4,3,3,4,3,3,3,4,3,3
%N Maximal number of distinct prime factors of any composite number between n-th and (n+1)-st primes.
%H Amiram Eldar, <a href="/A052298/b052298.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 46, prime(46) = 199, next prime is 211. In between, the number of prime factors for {200,201,...,210} is {2,2,2,2,3,2,2,2,2,2,4} of which the maximum is 4, which arises at 210. So a(46) = 4. [Corrected by _Sean A. Irvine_, Nov 04 2021]
%t Join[{0}, Max[PrimeNu[Range[First[#]+1, Last[#]-1]]]&/@Partition[ Prime[ Range[ 2, 110]], 2, 1]] (* _Harvey P. Dale_, Sep 26 2014 *)
%Y Cf. A052180, A052248, A052299.
%K nonn
%O 1,3
%A _Labos Elemer_, Feb 09 2000
%E Missing a(1)=0 inserted by _Sean A. Irvine_, Nov 04 2021
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