|
%I #22 May 28 2021 17:18:03
%S 2,3,4,6,8,9,12,15,16,27,30,32,33,36,39,42,64,81,84,87,90,93,96,108,
%T 111,114,117,120,123,128,243,246,249,252,255,256,258,270,273,276,279,
%U 282,285,324,327,330,333,336,339
%N Numbers k such that k does not divide binomial(2*k-4, k-2).
%C Previous name was: Numbers n such that (n-2)-nd Catalan number is not divisible by n.
%C Conjecture (confirmed, see links): sequence is union of powers of two > 1 (A000079) and 3 * A096304.
%H Charles R Greathouse IV, <a href="/A019469/b019469.txt">Table of n, a(n) for n = 1..10000</a>
%H Kevin Ryde, <a href="/A019469/a019469.txt">Proof of Wouter Meeussen's conjectured union</a>
%p A019469:=n->`if`(binomial(2*n-4,n-2) mod n <> 0,n,NULL): seq(A019469(n), n=1..400); # _Wesley Ivan Hurt_, Sep 13 2014
%t Select[Range[400],!Divisible[Binomial[2#-4,#-2],#]&] (* _Harvey P. Dale_, Aug 13 2015 *)
%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(1))); 0 \\ _Charles R Greathouse IV_, Nov 04 2016
%Y Cf. A000079, A096304, A000984.
%Y Complement of A019470.
%K nonn
%O 1,1
%A _Wouter Meeussen_
%E Name changed by _Wesley Ivan Hurt_, Sep 16 2014
|
