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A273777 Consider all ways of writing the n-th composite number as the product of two divisors d1*d2 = d3*d4 = ... where each divisor is larger than 1; a(n) is the maximum of the sums {d1 + d2, d3 + d4, ...}. 0
4, 5, 6, 6, 7, 8, 9, 8, 10, 11, 12, 10, 13, 14, 10, 15, 12, 16, 17, 18, 14, 19, 12, 20, 21, 16, 22, 23, 24, 18, 25, 26, 14, 27, 20, 28, 29, 16, 30, 22, 31, 32, 33, 24, 34, 18, 35, 36, 26, 37, 38, 39, 28, 40, 18, 41, 42, 30, 43, 44, 22, 45, 32, 46, 47, 20, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The divisors must be > 1 and < n.

For the minimum sums see A273227.

LINKS

Table of n, a(n) for n=1..67.

FORMULA

Let m = A002808(n). Then a(n) = A020639(m) + m / A020639(m).

EXAMPLE

a(14) = 14 because A002808(14) = 24 = 2*12 = 3*8 = 4*6 and 2+12 = 14 is the maximum sum.

MAPLE

with(numtheory):nn:=100:lst:={}:

for n from 1 to nn do:

it:=0:lst:={}:

d:=divisors(n):n0:=nops(d):

  if n0>2 then

  for i from 2 to n0-1 do:

   p:=d[i]:

    for j from i to n0-1 do:

      q:=d[j]:

       if p*q=n then

        lst:=lst union {p+q}:

        else

       fi:

     od:

    od:

    n0:=nops(lst):printf(`%d, `, lst[n0]):

   fi:

   od:

MATHEMATICA

Function[n, Max@ Map[Plus[#, n/#] &, Rest@ Take[#, Ceiling[Length[#]/2]]] &@ Divisors@ n] /@ Select[Range@ 120, CompositeQ] (* Michael De Vlieger, May 30 2016 *)

PROG

(PARI) lista(nn) = {forcomposite(n=2, nn, m = 0; fordiv(n, d, if ((d != 1) && (d != n), m = max(m, d+n/d)); ); print1(m, ", "); ); } \\ Michel Marcus, Sep 13 2017

CROSSREFS

Cf. A002808, A020639, A046343, A063655, A273227.

Sequence in context: A022911 A162310 A116962 * A023846 A046345 A004445

Adjacent sequences:  A273774 A273775 A273776 * A273778 A273779 A273780

KEYWORD

nonn

AUTHOR

Michel Lagneau, May 30 2016

EXTENSIONS

Name edited by Jon E. Schoenfield, Sep 12 2017

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)