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

1,4

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001405, A034974, A067434.

Sequence in context: A280472 A068063 A087181 * A316626 A269734 A066927

Adjacent sequences: A034970 A034971 A034972 * A034974 A034975 A034976

Keyword

nonn,easy,nice

Author

Labos Elemer

Status

approved