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 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 (list; graph; refs; listen; history; text; internal format)
 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 STATUS approved

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Last modified April 6 13:18 EDT 2020. Contains 333276 sequences. (Running on oeis4.)