A227902 - OEIS

%I #19 Apr 03 2021 19:04:34

%S 1,2,4,6,15,20,24,28,40,42,45,66,72,77,88,91,104,110,126,140,153,156,

%T 170,187,190,204,209,210,220,228,231,238,240,266,276,299,304,308,312,

%U 315,322,325,330,345,368,378,414,420,429,435,440,442,450,459,460,464,468,476,480

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

%C A014847 is a subsequence.

%H David A. Corneth, <a href="/A227902/b227902.txt">Table of n, a(n) for n = 1..10000</a>

%e triangular(6)=21, A000984(6)=924. Because 21 divides 924, 6 is in the sequence.

%t Select[Range[480], Mod[Binomial[2 #, #], # (# + 1)/2] == 0 &] (* _T. D. Noe_, Oct 16 2013 *)

%o (Python)

%o from sympy import binomial

%o for n in range(1, 444):

%o     CBC = binomial(2 * n, n)

%o     if not CBC % binomial(n + 1, 2):

%o        print(n, end=",")

%o (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 val(n, p) = my(r=0); while(n, r+=n\=p);r \\ _David A. Corneth_, Apr 03 2021

%Y Cf. A000984, A014847, A081766, A081767, A110493-A110496, A226047.

%K nonn,easy

%O 1,2

%A _Alex Ratushnyak_, Oct 14 2013