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A227902
Numbers n such that triangular(n) divides binomial(2n,n).
1
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
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
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Oct 14 2013
STATUS
approved