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A057245
Numbers n such that n | Sum_{k=1..n} k!.
6
1, 3, 9, 11, 33, 99
OFFSET
1,2
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.
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 *)
PROG
(GAP) Filtered([1..1500], n->Sum([1..n], k->Factorial(k)) mod n =0); # Muniru A Asiru, Oct 28 2018
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Robert G. Wilson v, Sep 21 2000
STATUS
approved