A293273 a(n) is the smallest positive k <> n such that f(k) is divisible by f(n) where f = A005132, or 0 if no such k exists.

2, 3, 8, 3, 9, 35, 43, 15, 20, 11, 28, 7, 32, 21, 83, 15, 69, 26, 152, 24, 116, 47, 44, 20, 48, 18, 43, 59, 30, 63, 20, 104, 41, 71, 39, 75, 72, 35, 35, 36, 33, 79, 92, 83, 96, 87, 100, 91, 245, 95, 239, 67, 276, 19, 119, 63, 109, 57, 103, 51, 185, 45, 139, 35, 145, 86, 415, 84, 192, 82, 184, 80, 180, 78, 176

Offset: 1

Author

Altug Alkan, Oct 10 2017

Keywords

• nonn
• easy

Comments

Conjecture: a(n) > 0 for all n.

Examples

			a(6) = 35 because A005132(35) = 78 is divisible by A005132(6) = 13 and 78 is the smallest positive number which is not equal to 6 with this property.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Logarithmic scatterplot of the first 100000 terms
• Rémy Sigrist, Scatterplot of the first 100000 terms of the first difference

Crossrefs

Cf. A005132, A057167.

Programs

Maple

N:= 10^4: # to use A005132(n) for n = 1..N
S:= {0}:
A5132:= Array(0..N):
A5132[0]:= 0:
for n from 1 to N do
  v:= A5132[n-1]-n;
  if v < 0 or member(v,S) then v:= A5132[n-1]+n fi;
  A5132[n]:= v;
  S:= S union {v};
od:
f:= proc(n) local k;
  for k from 1 to N do
    if k <> n and A5132[k] mod A5132[n] = 0 then return k fi
  od:
0
end proc:
Res:= NULL:
for n from 1 do
  v:= f(n);
  if v = 0 then break fi;
  Res:= Res,v;
od:
Res; # Robert Israel, Oct 10 2017