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

1, 2, 4, 6, 15, 20, 24, 28, 40, 42, 45, 66, 72, 77, 88, 91, 104, 110, 126, 140, 153, 156, 170, 187, 190, 204, 209, 210, 220, 228, 231, 238, 240, 266, 276, 299, 304, 308, 312, 315, 322, 325, 330, 345, 368, 378, 414, 420, 429, 435, 440, 442, 450, 459, 460, 464, 468, 476, 480

Offset

1,2

Comments

A014847 is a subsequence.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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

Prog

(Python)
from sympy import binomial
for n in range(1, 444):
    CBC = binomial(2 * n, n)
    if not CBC % binomial(n + 1, 2):
       print(n, end=", ")
(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 }
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Apr 03 2021

Crossrefs

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

Sequence in context: A275664 A349979 A192536 * A217525 A295615 A127679

Adjacent sequences: A227899 A227900 A227901 * A227903 A227904 A227905

Keyword

nonn,easy

Author

Alex Ratushnyak, Oct 14 2013

Status

approved