cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A057245 #44 Jun 09 2025 20:25:49
%S A057245 1,3,9,11,33,99
%N A057245 Numbers m such that m | Sum_{k=1..m} k!.
%C A057245 n such that A067462(n) = 0. - _T. D. Noe_, May 13 2010
%C A057245 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 A057245 n > 1 is in this sequence iff A049782(n) = 1. - _Max Alekseyev_, Apr 17 2016
%C A057245 If it exists, a(7) > 12000000. - _Bert Dobbelaere_, Oct 28 2018
%C A057245 If it exists, a(7) > 1.6*10^8. - _Giovanni Resta_, Nov 09 2018
%D A057245 Richard K. Guy, Unsolved Problems in Number Theory, Springer, Third Ed., 2004, Section B44.
%t A057245 a = 0; b = 1; k = 2; While[k < 250001, c = k*b - (k - 1) a;
%t A057245 If[ Mod[c, k] == 1, Print[k]]; a = b; b = c; k++] (* _Robert G. Wilson v_, Jun 15 2013 *)
%o A057245 (GAP) Filtered([1..1500],m->Sum([1..m],k->Factorial(k)) mod m = 0); # _Muniru A Asiru_, Oct 28 2018
%Y A057245 Cf. A007489, A049782, A064383.
%K A057245 nonn,hard,more
%O A057245 1,2
%A A057245 _Robert G. Wilson v_, Sep 21 2000