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

Author

Wouter Meeussen

Keywords

• nonn

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

Crossrefs

Complement of A019469. Cf. A000108.

Programs

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 *)

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])Charles R Greathouse IV, Nov 04 2016

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