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

10, 18, 21, 22, 27, 30, 33, 34, 35, 40, 42, 45, 52, 55, 56, 57, 58, 65, 66, 69, 70, 75, 77, 81, 82, 84, 85, 88, 90, 93, 94, 98, 100, 102, 105, 106, 108, 110, 115, 118, 119, 120, 121, 129, 132, 133, 135, 136, 138, 140, 141, 148, 152, 154, 155, 156, 161, 162, 164

Offset

1,1

Comments

Contains no primes. - Robert Israel, Aug 07 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

Maple

filter:= proc(n) local t, p, L, f, i, c;
  for f in ifactors(numtheory:-sigma(n))[2] do
     p:= f[1];
     L:= convert(n, base, p);
     t:= 0; c:= 0;
     for i from 1 to nops(L) do
       if 2*L[i]+c >= p then
         c:= 1; t:= t+1; if t >= f[2] then break fi;
       else
         c:= 0;
       fi
     od:
     if t < f[2] then return true fi;
  od;
  false
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 07 2018

Mathematica

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

Prog

(PARI) isok(n) = binomial(2*n, n) % sigma(n); \\ Michel Marcus, Nov 28 2013

Crossrefs

Sequence in context: A043758 A043767 A290002 * A055481 A213717 A333999

Adjacent sequences: A072989 A072990 A072991 * A072993 A072994 A072995

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 21 2002

Status

approved