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

6,1

Links

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A115061 A217834 A227877 * A046822 A129001 A029246

Adjacent sequences: A225864 A225865 A225866 * A225868 A225869 A225870

Keyword

nonn

Author

Vladimir Shevelev, May 18 2013

Extensions

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

Status

approved