A052299 Minimal number of distinct prime factors of any composite number between n-th and (n+1)-st primes.
1, 2, 1, 2, 1, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 1, 1, 2, 3, 2, 3, 2, 2, 2, 1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 1, 1, 2, 2, 3, 2, 2, 3, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 4, 2, 2
Offset: 2
Keywords
Examples
For n = 81: prime(81) = 419, prime(82) = 421. The intermediate range of composites includes only 420 = 4*3*5*7 having 4 distinct prime factors, so a(81) = 4.
Links
- Amiram Eldar, Table of n, a(n) for n = 2..10000
Programs
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Mathematica
Min[PrimeNu[Range[#[[1]]+1,#[[2]]-1]]]&/@Partition[Prime[ Range[ 2,110]],2,1] (* Harvey P. Dale, Mar 31 2012 *)
Extensions
Offset corrected by Sean A. Irvine, Nov 04 2021