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A120623 Numbers n such that the n-th Catalan number C(2n, n)/(n + 1) is divisible by n/3 but not divisible by n.

%I A120623 #13 Jun 07 2020 04:14:39
%S A120623 3,12,18,84,99,120,198,216,273,342,432,522,540,792,828,945,975,984,
%T A120623 990,1035,1071,1323,1377,1512,1548,1575,1710,1755,1863,2052,2106,2226,
%U A120623 2385,2442,2790,2928,3009,3015,3132,3198,3483,3672,3807,3915,3996,4212,4428
%N A120623 Numbers n such that the n-th Catalan number C(2n, n)/(n + 1) is divisible by n/3 but not divisible by n.
%H A120623 Chai Wah Wu, <a href="/A120623/b120623.txt">Table of n, a(n) for n = 1..10000</a>
%t A120623 fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(n(n + 1)/3)] && !IntegerQ[ Binomial[2n, n]/n]; Select[ Range@4463, fQ@# &]
%o A120623 (Python)
%o A120623 A120623_list, b = [], 1
%o A120623 for n in range(1, 10**5):
%o A120623     if b % n and not (3*b) % n:
%o A120623         A120623_list.append(n)
%o A120623     b = b*(4*n+2)//(n+2) # _Chai Wah Wu_, Mar 30 2016
%Y A120623 Cf. A000108, A014847, A120622.
%K A120623 nonn
%O A120623 1,1
%A A120623 _Robert G. Wilson v_, Jun 19 2006
%E A120623 Better description from _Joel B. Lewis_, Nov 15 2006