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A188795 a(n) counts all integers k in [2,floor(sqrt(n))] such that the number of divisors d>1 of n-k with k|(n-d) equals A188550(n). 1
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 3, 1, 2, 2, 3, 2, 1, 1, 1, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..10000

MAPLE

with(numtheory):

a:= proc(n) option remember; local c, h, k, m;

       m, c:= 0, 0;

       for k from 2 to floor(sqrt(n)) do

          h:= nops(select(x-> irem(x, k)=0,

              [seq (n-d, d=divisors(n-k) minus{1})]));

          if h=m then c:=c+1 elif h>m then m, c:= h, 1 fi

       od; c

    end:

seq(a(n), n=4..120);  # Alois P. Heinz, Apr 10 2011

MATHEMATICA

b[n_] := Max @ Table[Length @ Select[Table[n-d, {d, Divisors[n-k] // Rest} ], Mod[#, k] == 0&], {k, 2, Floor[Sqrt[n]]}];

a[n_] := a[n] = Count[Range[2, Floor[Sqrt[n]]], k_ /; Count[Rest @ Divisors[n-k], d_ /; Divisible[n-d, k]] == b[n]];

Table[a[n], {n, 4, 120}] (* Jean-Fran├žois Alcover, Mar 27 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A188550, A188579, A188794.

Sequence in context: A255507 A195052 A104637 * A058745 A275333 A108393

Adjacent sequences:  A188792 A188793 A188794 * A188796 A188797 A188798

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Apr 10 2011

STATUS

approved

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Last modified February 16 05:10 EST 2019. Contains 320140 sequences. (Running on oeis4.)