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A120303 Largest prime factor of Catalan number A000108(n). 2

%I

%S 2,5,7,7,11,13,13,17,19,19,23,23,23,29,31,31,31,37,37,41,43,43,47,47,

%T 47,53,53,53,59,61,61,61,67,67,71,73,73,73,79,79,83,83,83,89,89,89,89,

%U 97,97,101,103,103,107,109,109,113,113,113,113,113,113,113,127,127,131,131

%N Largest prime factor of Catalan number A000108(n).

%C All prime numbers (except 3) are present in this sequence in their natural order with repetition. The number of repetitions is equal to A028334(n): differences between consecutive primes, divided by 2. - _Alexander Adamchuk_, Jul 30 2006

%C For p>3 a((p+1)/2) = p and all a(n) = p for n >= (p+1)/2 until the first occurrence of the next prime q = NextPrime(p) at a((q+1)/2) = q. - _Alexander Adamchuk_, Dec 27 2013

%F a(n) = A060308(n) = A060265(n) for n>2.

%F a(n) = A006530(A000108(n)). - _Michel Marcus_, Nov 14 2015

%t Table[Max[FactorInteger[(2n)!/n!/(n+1)! ]],{n,2,100}]

%t FactorInteger[CatalanNumber[#]][[-1,1]]&/@Range[2,70] (* _Harvey P. Dale_, May 02 2017 *)

%o (PARI) a(n) = vecmax(factor(binomial(2*n, n)/(n+1))[,1]); \\ _Michel Marcus_, Nov 14 2015

%o (PARI) a(n)=if(n>2,precprime(2*n),2) \\ _Charles R Greathouse IV_, Nov 17 2015

%Y Cf. A000108, A006530, A020482, A028334, A060265, A060308, A152765.

%K nonn

%O 2,1

%A _Alexander Adamchuk_, Jul 13 2006

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Last modified November 15 15:59 EST 2018. Contains 317239 sequences. (Running on oeis4.)