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A067434 Number of distinct prime factors in binomial(2*n,n). 16
1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 9, 9, 10, 10, 10, 9, 10, 10, 10, 10, 12, 13, 12, 12, 13, 14, 14, 14, 14, 14, 15, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 19, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 23, 24, 23, 23, 23, 23, 24, 24, 24, 25, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = A001221(A000984(n)) = length of n-th row in A226078. - Reinhard Zumkeller, May 25 2013

LINKS

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

FORMULA

a(n) ~ kn/log n, with k = log 4. - Charles R Greathouse IV, May 25 2013

MAPLE

a := n -> nops(numtheory:-factorset(binomial(2*n, n))):

seq(a(n), n=1..76); # Peter Luschny, Oct 31 2015

MATHEMATICA

Table[Length[FactorInteger[Binomial[2 n, n]]], {n, 100}] (* T. D. Noe, Aug 17 2011 *)

PROG

(Haskell)

a067434 = a001221 . a000984 -- Reinhard Zumkeller, May 25 2013

(PARI) a(n)=omega(binomial(2*n, n)) \\ Charles R Greathouse IV, May 25 2013

(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s

a(n)=my(s); forprime(p=2, 2*n, if(valp(2*n, p)>2*valp(n, p), s++)); s \\ Charles R Greathouse IV, May 25 2013

CROSSREFS

Cf. A193990, A193991 (number of prime factors <= n and > n).

Sequence in context: A082479 A090616 A186704 * A336348 A177357 A320297

Adjacent sequences:  A067431 A067432 A067433 * A067435 A067436 A067437

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Feb 23 2002

STATUS

approved

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Last modified September 25 18:21 EDT 2020. Contains 337344 sequences. (Running on oeis4.)