A057245 Numbers m such that m | Sum_{k=1..m} k!.

1, 3, 9, 11, 33, 99

Offset: 1

Author

Robert G. Wilson v, Sep 21 2000

Keywords

• nonn
• hard
• more

Comments

n such that A067462(n) = 0. - T. D. Noe, May 13 2010

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

n > 1 is in this sequence iff A049782(n) = 1. - Max Alekseyev, Apr 17 2016

If it exists, a(7) > 12000000. - Bert Dobbelaere, Oct 28 2018

If it exists, a(7) > 1.6*10^8. - Giovanni Resta, Nov 09 2018

References

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

Crossrefs

Cf. A007489, A049782, A064383.

Programs

GAP

Filtered([1..1500],m->Sum([1..m],k->Factorial(k)) mod m = 0); # Muniru A Asiru, Oct 28 2018

Mathematica

a = 0; b = 1; k = 2; While[k < 250001, c = k*b - (k - 1) a;
If[ Mod[c, k] == 1, Print[k]]; a = b; b = c; k++] (* Robert G. Wilson v, Jun 15 2013 *)