A034973 - OEIS

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

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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 *)