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

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, 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, 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

Offset: 1

Author

Max Alekseyev, Mar 09 2008

Keywords

• nonn

Comments

This sequence is well-defined.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Romanian Master in Mathematics Contest, Problem 3, Bucharest, 2007.

Crossrefs

Cf. A129795, A138255, A138256, A138257, A138259, A138260, A138261, A138262, A138263.

Programs

Maple

N:= 100: # for a(1)..a(N)
V:= Vector(N):
count:= 0: missing:= {$1..N}:
Q:= ilcm(seq(i,i=1..N)):
for m from 1 while count < N do
  v:= floor(5^m/m);
  r:= igcd(v,Q);
  d:= select(t -> r mod t = 0, missing);
  missing:= missing minus d;
  count:= count+nops(d);
  V[convert(d,list)]:= m;
od:
convert(V,list); # Robert Israel, Aug 27 2020

Mathematica

a[n_]:=Module[{m=1},While[!Divisible[Floor[5^m/m],n],m++];m];Array[a,82] (* James C. McMahon, Jun 05 2025 *)