A057245 - OEIS

%I #41 Nov 09 2018 10:18:29

%S 1,3,9,11,33,99

%N Numbers n such that n | Sum_{k=1..n} k!.

%C n such that A067462(n) = 0. - _T. D. Noe_, May 13 2010

%C For any terms in this sequence, their LCM also belongs to this sequence. Term a(7), if it exists, is prime. - _Max Alekseyev_, Oct 14 2012

%C n > 1 is in this sequence iff A049782(n) = 1. - _Max Alekseyev_, Apr 17 2016

%C If it exists, a(7) > 12000000. - _Bert Dobbelaere_, Oct 28 2018

%C If it exists, a(7) > 1.6*10^8. - _Giovanni Resta_, Nov 09 2018

%D Richard K. Guy, Unsolved Problems in Number Theory, Springer, Third Ed., 2004, Section B44.

%t a = 0; b = 1; k = 2; While[k < 250001, c = k*b - (k - 1) a;

%t If[ Mod[c, k] == 1, Print[k]]; a = b; b = c; k++] (* _Robert G. Wilson v_, Jun 15 2013 *)

%o (GAP) Filtered([1..1500],n->Sum([1..n],k->Factorial(k)) mod n =0); # _Muniru A Asiru_, Oct 28 2018

%Y Cf. A007489, A049782, A064383.

%K nonn,hard,more

%O 1,2

%A _Robert G. Wilson v_, Sep 21 2000