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 A013584 Smallest m such that 0!+1!+...+(m-1)! is divisible by n, or 0 if no such m exists. 4
 1, 2, 0, 3, 4, 0, 6, 0, 0, 4, 6, 0, 0, 6, 0, 0, 5, 0, 7, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 5, 0, 0, 22, 7, 0, 0, 16, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 12, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 42, 22, 0, 0, 6, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Robert Israel, Nov 14 2016: (Start) a(n) < n for n > 2. If a(n) = 0, then a(mn) = 0 for all m>=2. (End) REFERENCES M. R. Mudge, Smarandache Notions Journal, University of Craiova, Vol. VII, No. 1, 1996. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MAPLE f:= proc(n) local t, r, m;   r:= 1; t:= 1;   for m from 1 do     r:= r*m mod n;     if r = 0 then return 0 fi;     t:= t + r mod n;     if t = 0 then return m+1 fi;   od; end proc: f(1):= 1: map(f, [\$1..100]); # Robert Israel, Nov 14 2016 MATHEMATICA a[n_] := Module[{t, r, m}, r = 1; t = 1; For[m = 1, True, m++, r = Mod[r*m, n]; If[r == 0, Return[0]]; t = Mod[t+r, n]; If[t == 0, Return[m+1]]]]; Array[a, 100] (* Jean-François Alcover, Apr 12 2019, after Robert Israel *) CROSSREFS Cf. A003422, A013585, A049044, A049045, A275608. Sequence in context: A117909 A261094 A091538 * A307320 A137372 A212844 Adjacent sequences:  A013581 A013582 A013583 * A013585 A013586 A013587 KEYWORD nonn AUTHOR Michael R. Mudge (Amsorg(AT)aol.com) STATUS approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)