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

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, 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, 4, 5, 6, 6, 8, 4, 4, 6, 8, 3, 4, 6, 6, 8, 6, 3, 5, 4, 8, 6, 10

Offset: 6

Author

Vladimir Shevelev, May 18 2013

Keywords

• nonn

Links

• Peter J. C. Moses, Table of n, a(n) for n = 6..10005

Programs

Maple

A225867 := proc(n)
    local a,k,nd ;
    a := 0 ;
    for k from 2 to n/2-1 do
        nd := 0 ;
        for d in numtheory[divisors](n+k) minus {1} do
            if modp(n+d,k) = 0 then
                nd := nd+1;
            end if;
        end do:
        a := max(a,nd) ;
    end do:
    a ;
end proc: # R. J. Mathar, Jul 04 2013

Mathematica

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 *)

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

Extensions

Extended from a(14) by Peter J. C. Moses, May 18 2013