A225867 - OEIS

%I #21 Nov 25 2014 16:38:14

%S 3,2,2,3,4,1,3,3,4,4,3,2,4,3,4,4,6,2,3,4,4,4,4,2,5,3,3,6,6,4,4,4,6,4,

%T 4,2,4,5,6,5,8,2,3,4,4,6,4,3,6,6,4,6,8,2,5,5,6,4,4,4,6,4,6,8,9,2,4,5,

%U 4,5,6,6,8,4,4,6,8,3,4,6,6,8,6,3,5,4,8,6,10

%N a(n) = max_{2<=k<=(n-2)/2} sum_{d>1: d|n+k, k|n+d}1.

%H Peter J. C. Moses, <a href="/A225867/b225867.txt">Table of n, a(n) for n = 6..10005</a>

%p A225867 := proc(n)

%p     local a,k,nd ;

%p     a := 0 ;

%p     for k from 2 to n/2-1 do

%p         nd := 0 ;

%p         for d in numtheory[divisors](n+k) minus {1} do

%p             if modp(n+d,k) = 0 then

%p                 nd := nd+1;

%p             end if;

%p         end do:

%p         a := max(a,nd) ;

%p     end do:

%p     a ;

%p end proc: # _R. J. Mathar_, Jul 04 2013

%t Table[Max[Map[Count[(n+Rest[Divisors[n+#]])/#,_Integer]&,Range[2,Floor[(n-2)/2]]]],{n,6,105}] (* _Peter J. C. Moses_, Jun 27 2013 *)

%o (PARI) a(n)=my(t); for(k=2,n\2-1, t=max(sumdiv(n+k,d,(n+d)%k==0 && d>1),t)); t \\ _Charles R Greathouse IV_, Nov 25 2014

%K nonn

%O 6,1

%A _Vladimir Shevelev_, May 18 2013

%E Extended from a(14) by _Peter J. C. Moses_, May 18 2013