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A260640 Numbers n such that binomial(3*n,n) == 0 (mod n).

%I A260640 #20 Sep 08 2022 08:46:13
%S A260640 1,3,6,12,21,35,44,55,60,70,78,88,90,99,102,110,117,119,120,133,156,
%T A260640 171,176,180,184,204,207,220,225,230,231,234,238,240,247,252,255,285,
%U A260640 286,300,312,341,342,348,360,368,372,391,403,408,414,425,434,460,462,465,468,481,483,494,495,504,506,510,550,555,561,572,574,585,600
%N A260640 Numbers n such that binomial(3*n,n) == 0 (mod n).
%C A260640 See A014847 for the analog for 2n.
%H A260640 Chai Wah Wu, <a href="/A260640/b260640.txt">Table of n, a(n) for n = 1..10000</a>
%H A260640 M. Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP Scripts for Miscellaneous Math Problems</a>, sect. III: Binomial coefficients modulo integers, binomod.gp (v.1.4, 11/2015).
%t A260640 Select[Range@ 600, Mod[Binomial[3 #, #], #] == 0 &] (* _Michael De Vlieger_, Nov 12 2015 *)
%o A260640 (PARI) for(n=1,999,binomod(3*n,n,n)==0&&print1(n",")) \\ Using binomod.gp by M. Alekseyev, cf. links.
%o A260640 (Python)
%o A260640 from __future__ import division
%o A260640 A260640_list, b = [], 3
%o A260640 for n in range(1,10**3):
%o A260640     if not b % n:
%o A260640         A260640_list.append(n)
%o A260640     b = b*3*(3*n+2)*(3*n+1)//((2*n+2)*(2*n+1)) # _Chai Wah Wu_, Jan 27 2016
%o A260640 (Magma) [n: n in [1..600] |Binomial(3*n,n) mod n eq 0]; // _Vincenzo Librandi_, Jan 29 2016
%Y A260640 Cf. A260636, A080469, A109641, A109642, A014847.
%K A260640 nonn
%O A260640 1,2
%A A260640 _M. F. Hasler_, Nov 11 2015