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A072992 Numbers n such that sigma(n) does not divide C(2n,n). 1

%I #16 Aug 09 2018 03:24:49

%S 10,18,21,22,27,30,33,34,35,40,42,45,52,55,56,57,58,65,66,69,70,75,77,

%T 81,82,84,85,88,90,93,94,98,100,102,105,106,108,110,115,118,119,120,

%U 121,129,132,133,135,136,138,140,141,148,152,154,155,156,161,162,164

%N Numbers n such that sigma(n) does not divide C(2n,n).

%C Contains no primes. - _Robert Israel_, Aug 07 2018

%H Robert Israel, <a href="/A072992/b072992.txt">Table of n, a(n) for n = 1..10000</a>

%F It seems that a(n) is asymptotic to C*n with C=2.8...

%p filter:= proc(n) local t,p,L,f,i,c;

%p for f in ifactors(numtheory:-sigma(n))[2] do

%p p:= f[1];

%p L:= convert(n,base,p);

%p t:= 0; c:= 0;

%p for i from 1 to nops(L) do

%p if 2*L[i]+c >= p then

%p c:= 1; t:= t+1; if t >= f[2] then break fi;

%p else

%p c:= 0;

%p fi

%p od:

%p if t < f[2] then return true fi;

%p od;

%p false

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Aug 07 2018

%t fQ[n_] := Mod[ Binomial[2n, n], DivisorSigma[1, n]] > 0; Select[ Range@164, fQ] (* _Robert G. Wilson v_, Aug 07 2018 *)

%o (PARI) isok(n) = binomial(2*n, n) % sigma(n); \\ _Michel Marcus_, Nov 28 2013

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Aug 21 2002

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)