A052298 Maximal number of distinct prime factors of any composite number between n-th and (n+1)-st primes.
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, 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, 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
Offset: 1
Keywords
Examples
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]
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Join[{0}, Max[PrimeNu[Range[First[#]+1, Last[#]-1]]]&/@Partition[ Prime[ Range[ 2, 110]], 2, 1]] (* Harvey P. Dale, Sep 26 2014 *)
Extensions
Missing a(1)=0 inserted by Sean A. Irvine, Nov 04 2021