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A138258 Smallest positive integer m such that n divides [5^m/m] (=A129795(m)).

%I A138258 #18 Jun 06 2025 08:36:27
%S A138258 1,2,2,2,1,2,6,7,7,7,22,2,4,6,7,13,16,7,10,7,6,31,55,7,5,4,19,6,15,7,
%T A138258 6,17,31,16,13,7,36,10,4,7,3,6,42,31,7,55,51,13,43,26,16,4,52,19,31,
%U A138258 13,18,15,27,7,31,6,13,17,17,31,9,16,67,13,11,7,66,36,26,18,31,4,9,13,56,61
%N A138258 Smallest positive integer m such that n divides [5^m/m] (=A129795(m)).
%C A138258 This sequence is well-defined.
%H A138258 Robert Israel, <a href="/A138258/b138258.txt">Table of n, a(n) for n = 1..10000</a>
%H A138258 Romanian Master in Mathematics Contest, <a href="https://artofproblemsolving.com/community/c6h187665">Problem 3</a>, Bucharest, 2007.
%p A138258 N:= 100: # for a(1)..a(N)
%p A138258 V:= Vector(N):
%p A138258 count:= 0: missing:= {$1..N}:
%p A138258 Q:= ilcm(seq(i,i=1..N)):
%p A138258 for m from 1 while count < N do
%p A138258   v:= floor(5^m/m);
%p A138258   r:= igcd(v,Q);
%p A138258   d:= select(t -> r mod t = 0, missing);
%p A138258   missing:= missing minus d;
%p A138258   count:= count+nops(d);
%p A138258   V[convert(d,list)]:= m;
%p A138258 od:
%p A138258 convert(V,list); # _Robert Israel_, Aug 27 2020
%t A138258 a[n_]:=Module[{m=1},While[!Divisible[Floor[5^m/m],n],m++];m];Array[a,82] (* _James C. McMahon_, Jun 05 2025 *)
%Y A138258 Cf. A129795, A138255, A138256, A138257, A138259, A138260, A138261, A138262, A138263.
%K A138258 nonn
%O A138258 1,2
%A A138258 _Max Alekseyev_, Mar 09 2008