%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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