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%I #36 Oct 20 2017 23:11:40
%S 2,3,8,3,9,35,43,15,20,11,28,7,32,21,83,15,69,26,152,24,116,47,44,20,
%T 48,18,43,59,30,63,20,104,41,71,39,75,72,35,35,36,33,79,92,83,96,87,
%U 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
%N 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.
%C Conjecture: a(n) > 0 for all n.
%H Robert Israel, <a href="/A293273/b293273.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A293273/a293273.png">Logarithmic scatterplot of the first 100000 terms</a>
%H Rémy Sigrist, <a href="/A293273/a293273_1.png">Scatterplot of the first 100000 terms of the first difference</a>
%e 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.
%p N:= 10^4: # to use A005132(n) for n = 1..N
%p S:= {0}:
%p A5132:= Array(0..N):
%p A5132[0]:= 0:
%p for n from 1 to N do
%p v:= A5132[n-1]-n;
%p if v < 0 or member(v,S) then v:= A5132[n-1]+n fi;
%p A5132[n]:= v;
%p S:= S union {v};
%p od:
%p f:= proc(n) local k;
%p for k from 1 to N do
%p if k <> n and A5132[k] mod A5132[n] = 0 then return k fi
%p od:
%p 0
%p end proc:
%p Res:= NULL:
%p for n from 1 do
%p v:= f(n);
%p if v = 0 then break fi;
%p Res:= Res,v;
%p od:
%p Res; # _Robert Israel_, Oct 10 2017
%Y Cf. A005132, A057167.
%K nonn,easy
%O 1,1
%A _Altug Alkan_, Oct 10 2017
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