A226182 a(n) is the smallest integer k >= 2 such that the number of divisors d>1 of n + k with k|n + d equals A225867(n).

2, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 3, 2, 2, 4, 3, 2, 2, 3, 5, 2, 3, 2, 3, 2, 2, 4, 3, 2, 5, 4, 3, 2, 3, 2, 3, 2, 2, 4, 3, 2, 2, 2, 7, 2, 3, 2, 2, 2, 5, 4, 3, 2, 4, 4, 2, 2, 3, 2, 5, 6, 3, 4, 3, 2, 4, 8, 2, 2, 5, 4, 7, 2, 2, 4, 3, 2, 2, 4, 5, 2, 3, 2, 2, 6, 7, 4

Offset

6,1

Links

Peter J. C. Moses, Table of n, a(n) for n = 6..3005

Example

Let n = 33. We begin with k = 2. Divisors>1 of 33 + 2 = 35 are d = 5,7,35. For all d, 33 + d is divisible by k = 2. But the number of such d is 3, while A225867(33)= 6. Therefore, a(33) > 2. Consider now k = 3. Divisors>1 of 33 + 3 = 36 are 2,3,4,6,9,12,18,36, but only for d = 3,6,9,12,18,36, 33 + d is divisible by k = 3. Since we have exactly A225867(33) = 6 such divisors, then k = 3 is required and a(33) = 3.

Maple

A226182 := proc(n)
    local ak, k, nd, kpiv ;
    ak := 0 ;
    kpiv := 2 ;
    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:
        if nd > ak then
            ak := max(ak, nd) ;
            kpiv := k ;
        end if;
    end do:
    kpiv ;
end proc: # R. J. Mathar, Jul 04 2013

Mathematica

Table[NestWhile[#+1&, 2, Max[Map[Count[(n+Rest[Divisors[n+#]])/#, _Integer]&, Range[2, Floor[(n-2)/2]]]]-Count[(n+Rest[Divisors[n+#]])/#, _Integer] =!= 0&], {n, 6, 55}] (* Peter J. C. Moses, Jun 03 2013 *)

Crossrefs

Cf. A225867, A225868, A188550, A188794.

Sequence in context: A176775 A175778 A357039 * A099774 A305973 A290978

Adjacent sequences: A226179 A226180 A226181 * A226183 A226184 A226185

Keyword

nonn

Author

Vladimir Shevelev, May 30 2013

Status

approved