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

1,3

Links

Table of n, a(n) for n=1..106.

Example

n=46, p(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]

Mathematica

Max[PrimeNu[Range[First[#]+1, Last[#]-1]]]&/@Partition[ Prime[ Range[ 2, 110]], 2, 1] (* Harvey P. Dale, Sep 26 2014 *)

Crossrefs

Cf. A052180, A052248.

Sequence in context: A359309 A147793 A352201 * A366441 A179938 A081412

Adjacent sequences: A052295 A052296 A052297 * A052299 A052300 A052301

Keyword

nonn

Author

Labos Elemer, Feb 09 2000

Extensions

Missing a(1)=0 inserted by Sean A. Irvine, Nov 04 2021

Status

approved