A188794 a(n) is the smallest integer k >= 2 such that the number of divisors d>1 of n-k with k|(n-d) equals A188550(n).

2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 5, 2, 3, 4, 2, 2, 3, 2, 3, 2, 5, 4, 2, 2, 3, 4, 2, 2, 3, 2, 3, 2, 2, 3, 7, 2, 3, 4, 2, 2, 5, 2, 3, 2, 3, 4, 2, 2, 3, 4, 5, 2, 2, 4, 3, 2, 2, 2, 3, 2, 3, 4, 2, 6, 2, 2, 3, 2, 3, 4, 5, 2, 3, 4, 2, 2, 7, 2, 3, 4, 5, 6, 2, 2, 3, 4, 2, 2, 3, 8, 5, 2, 2, 3, 4, 2, 3, 2, 3, 2

Offset

4,1

Comments

a(n) <= floor(sqrt(n)) follows from the definition of A188550.

Links

Alois P. Heinz, Table of n, a(n) for n = 4..20004

Maple

with(numtheory):
a:= proc(n) local h, i, k, m;
       m, i:= 0, 0;
       for k from 2 to floor(sqrt(n)) do
          h:= nops(select(x-> irem(x, k)=0,
              [seq (n-d, d=divisors(n-k) minus{1})]));
          if h>m then m, i:= h, k fi
       od; i
    end:
seq(a(n), n=4..120);  # Alois P. Heinz, Apr 10 2011

Mathematica

a[n_] := Module[{h, i = 0, k, m = 0}, For[k = 2, k <= Floor[Sqrt[n]], k++, h = Length[Select[Table[n-d, {d, Rest[Divisors[n-k]]}], Mod[#, k] == 0&]]; If[h > m, {m, i} = {h, k}]]; i];
a /@ Range[4, 120] (* Jean-François Alcover, Oct 28 2020, after Alois P. Heinz *)

Crossrefs

Cf. A188550, A188579.

Sequence in context: A262954 A262813 A360964 * A161966 A187188 A358618

Adjacent sequences: A188791 A188792 A188793 * A188795 A188796 A188797

Keyword

nonn,look

Author

Vladimir Shevelev, Apr 10 2011

Status

approved