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A013584
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Smallest m such that 0!+1!+...+(m-1)! is divisible by n, or 0 if no such m exists.
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4
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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
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OFFSET
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1,2
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COMMENTS
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a(n) < n for n > 2.
If a(n) = 0, then a(mn) = 0 for all m>=2. (End)
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REFERENCES
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M. R. Mudge, Smarandache Notions Journal, University of Craiova, Vol. VII, No. 1, 1996.
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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]]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Michael R. Mudge (Amsorg(AT)aol.com)
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STATUS
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approved
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