A034973 Number of distinct prime factors in central binomial coefficients C(n, floor(n/2)), the terms of A001405.

0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 13, 13, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 14, 14, 15, 15, 15, 15, 16

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy
• nice

Comments

Sequence is not monotonic. E.g., a(44)=10, a(45)=9 and a(46)=10. The number of prime factors of n! is pi(n), but these numbers are lower.

Prime factors are counted without multiplicity. - Harvey P. Dale, May 20 2012

Examples

			a(25) = omega(binomial(25,12)) = omega(5200300) = 6 because the prime factors are 2, 5, 7, 17, 19, 23.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001405, A034974, A067434.

Programs

Mathematica

Table[PrimeNu[Binomial[n,Floor[n/2]]],{n,90}] (* Harvey P. Dale, May 20 2012 *)

PARI

a(n)=omega(binomial(n,n\2)) \\ Charles R Greathouse IV, Apr 29 2015