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Numbers k that divide binomial(2*k-4, k-2).
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%I #34 Dec 25 2022 02:16:42

%S 1,5,7,10,11,13,14,17,18,19,20,21,22,23,24,25,26,28,29,31,34,35,37,38,

%T 40,41,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,

%U 65,66,67,68,69,70,71,72,73,74,75,76,77,78,79

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

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

%C For k in this sequence, convex k-gons have a number of triangulations that is divisible by k. - _David Eppstein_, Dec 24 2022

%H Charles R Greathouse IV, <a href="/A019470/b019470.txt">Table of n, a(n) for n = 1..10000</a>

%p 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

%t Select[Range[100],Divisible[Binomial[2#-4,#-2],#]&] (* _Giorgos Kalogeropoulos_, Aug 20 2021 *)

%o (PARI) valp(n,p)=my(s); while(n\=p, s+=n); s

%o bin(n,p)=valp(2*n,p)-2*valp(n,p)

%o 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

%Y Complement of A019469. Cf. A000108.

%K nonn

%O 1,2

%A _Wouter Meeussen_

%E More terms from _Wesley Ivan Hurt_, Sep 13 2014

%E Offset corrected by _Robert Israel_, Sep 14 2014

%E Name changed by _Wesley Ivan Hurt_, Sep 16 2014