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

Author

Vladimir Shevelev, Apr 10 2011

Keywords

• nonn
• look

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

Crossrefs

Cf. A188550, A188579.

Programs

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 *)