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A072992 Numbers n such that sigma(n) does not divide C(2n,n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 13 11:24 EDT 2021. Contains 342936 sequences. (Running on oeis4.)