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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, 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 (list; graph; refs; listen; history; text; internal format)
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: A242879 A176775 A175778 * A099774 A305973 A290978

Adjacent sequences:  A226179 A226180 A226181 * A226183 A226184 A226185

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 30 2013

STATUS

approved

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Last modified July 23 19:33 EDT 2019. Contains 325263 sequences. (Running on oeis4.)