

A034973


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


11



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


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



