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A227902 Numbers n such that triangular(n) divides binomial(2n,n).

%I A227902 #19 Apr 03 2021 19:04:34
%S A227902 1,2,4,6,15,20,24,28,40,42,45,66,72,77,88,91,104,110,126,140,153,156,
%T A227902 170,187,190,204,209,210,220,228,231,238,240,266,276,299,304,308,312,
%U A227902 315,322,325,330,345,368,378,414,420,429,435,440,442,450,459,460,464,468,476,480
%N A227902 Numbers n such that triangular(n) divides binomial(2n,n).
%C A227902 A014847 is a subsequence.
%H A227902 David A. Corneth, <a href="/A227902/b227902.txt">Table of n, a(n) for n = 1..10000</a>
%e A227902 triangular(6)=21, A000984(6)=924. Because 21 divides 924, 6 is in the sequence.
%t A227902 Select[Range[480], Mod[Binomial[2 #, #], # (# + 1)/2] == 0 &] (* _T. D. Noe_, Oct 16 2013 *)
%o A227902 (Python)
%o A227902 from sympy import binomial
%o A227902 for n in range(1, 444):
%o A227902     CBC = binomial(2 * n, n)
%o A227902     if not CBC % binomial(n + 1, 2):
%o A227902        print(n, end=",")
%o A227902 (PARI) is(n) = { my(f = factor(binomial(n+1, 2))); for(i = 1, #f~, if(val(2*n, f[i, 1]) - 2*val(n, f[i, 1]) < f[i, 2], return(0) ) ); 1 }
%o A227902 val(n, p) = my(r=0); while(n, r+=n\=p);r \\ _David A. Corneth_, Apr 03 2021
%Y A227902 Cf. A000984, A014847, A081766, A081767, A110493-A110496, A226047.
%K A227902 nonn,easy
%O A227902 1,2
%A A227902 _Alex Ratushnyak_, Oct 14 2013