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%I #22 Dec 25 2016 00:34:08
%S 0,0,1,1,2,3,4,3,4,4,5,5,6,7,9,7,8,8,10,9,10,10,11,11,11,12,12,11,13,
%T 13,14,11,13,14,14,13,14,14,16,15,16,18,19,19,19,19,21,19,20,19,21,20,
%U 21,21,21,19,20,20,22,22,24,25,25,23,23,23,24,24,27,26,27,25,27,28,29,28
%N Bigomega of the n-th Catalan number: a(n) = A001222(A000108(n)).
%C It is easy to show that a(n) is between n/log(n) and 2n/log(n) (for n>n0), cf. [Campbell 1984]. The sequence A137687, roughly the middle of this interval, is a fair approximation for A081399. See A137686 for the (signed) difference of the two sequences.
%H M. F. Hasler, <a href="/A081399/b081399.txt">Table of n, a(n) for n = 0..3000</a>.
%H Douglas M. Campbell, <a href="http://www.jstor.org/stable/2689673">The Computation of Catalan Numbers</a>, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.
%F a(n)=A001222[A000108(n)]
%p with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(2*n,n)/(1+n)) fi end: seq(a(n), n=0..75); # _Zerinvary Lajos_, Apr 11 2008
%t a[n_] := PrimeOmega[ CatalanNumber[n]]; Table[a[n], {n, 0, 75}] (* _Jean-François Alcover_, Jul 02 2013 *)
%o (PARI) A081399(n)=bigomega(prod(i=2,n,(n+i)/i)) \\ _M. F. Hasler_, Feb 06 2008
%Y Cf. A001222, A000108, A022559, A023816, A048621, A081405, A120626, A137686-A137687.
%Y Cf. A080405.
%K nonn,easy
%O 0,5
%A _Labos Elemer_, Mar 28 2003
%E Edited and extended by _M. F. Hasler_, Feb 06 2008
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