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A225867 a(n) = max_{2<=k<=(n-2)/2} sum_{d>1: d|n+k, k|n+d}1.

%I A225867 #21 Nov 25 2014 16:38:14
%S A225867 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 A225867 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 A225867 4,5,6,6,8,4,4,6,8,3,4,6,6,8,6,3,5,4,8,6,10
%N A225867 a(n) = max_{2<=k<=(n-2)/2} sum_{d>1: d|n+k, k|n+d}1.
%H A225867 Peter J. C. Moses, <a href="/A225867/b225867.txt">Table of n, a(n) for n = 6..10005</a>
%p A225867 A225867 := proc(n)
%p A225867     local a,k,nd ;
%p A225867     a := 0 ;
%p A225867     for k from 2 to n/2-1 do
%p A225867         nd := 0 ;
%p A225867         for d in numtheory[divisors](n+k) minus {1} do
%p A225867             if modp(n+d,k) = 0 then
%p A225867                 nd := nd+1;
%p A225867             end if;
%p A225867         end do:
%p A225867         a := max(a,nd) ;
%p A225867     end do:
%p A225867     a ;
%p A225867 end proc: # _R. J. Mathar_, Jul 04 2013
%t A225867 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 A225867 (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 A225867 nonn
%O A225867 6,1
%A A225867 _Vladimir Shevelev_, May 18 2013
%E A225867 Extended from a(14) by _Peter J. C. Moses_, May 18 2013