A019470 Numbers k that divide binomial(2*k-4, k-2).

1, 5, 7, 10, 11, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 34, 35, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset

1,2

Comments

Old name was: (n-2)-nd Catalan number is divisible by n.

For k in this sequence, convex k-gons have a number of triangulations that is divisible by k. - David Eppstein, Dec 24 2022

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Maple

A019470:=n->`if`(binomial(2*n-4, n-2) mod n = 0, n, NULL): seq(A019470(n), n=1..70); # Wesley Ivan Hurt, Sep 13 2014

Mathematica

Select[Range[100], Divisible[Binomial[2#-4, #-2], #]&] (* Giorgos Kalogeropoulos, Aug 20 2021 *)

Prog

(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
bin(n, p)=valp(2*n, p)-2*valp(n, p)
is(n)=my(f=factor(n)); for(i=1, #f~, if(bin(n-2, f[i, 1])<f[i, 2], return(0))); 1 \\ Charles R Greathouse IV, Nov 04 2016

Crossrefs

Complement of A019469. Cf. A000108.

Sequence in context: A028786 A282391 A080760 * A161827 A063547 A064479

Adjacent sequences: A019467 A019468 A019469 * A019471 A019472 A019473

Keyword

nonn

Author

Wouter Meeussen

Extensions

More terms from Wesley Ivan Hurt, Sep 13 2014

Offset corrected by Robert Israel, Sep 14 2014

Name changed by Wesley Ivan Hurt, Sep 16 2014

Status

approved