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A273227 Consider all ways of writing the n-th composite number as the product of two divisors d1*d2 = d3*d4 = ...; a(n) is the minimum of the sums {d1 + d2, d3 + d4, ...}. 3
4, 5, 6, 6, 7, 7, 9, 8, 8, 9, 9, 10, 13, 10, 10, 15, 12, 11, 11, 12, 14, 19, 12, 12, 21, 16, 13, 13, 15, 14, 25, 14, 14, 15, 20, 17, 15, 16, 15, 22, 31, 16, 33, 16, 16, 18, 17, 21, 26, 17, 17, 39, 20, 23, 18, 19, 18, 18, 43, 19, 22, 45, 32, 19, 19, 20, 27, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = A046343(n) if n is semiprime.

This sequence is included in A063655. - Giovanni Resta, May 18 2016

a(n) >= 2 * sqrt(A002808(n)). - David A. Corneth, May 20 2016

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(14) = 10 because A002808(14) = 24 = 2*12 = 3*8 = 4*6 and 4+6 = 10 is the minimum 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:

    printf(`%d, `, lst[1]):

   fi:

   od:

MATHEMATICA

Function[n, If[OddQ@ Length@ #, 2 Sqrt@ n, Total@ Take[#, {Length[#]/2, Length[#]/2 + 1}]] &@ Divisors@ n] /@ Select[Range@ 93, CompositeQ] (* Michael De Vlieger, May 20 2016 *)

msd[n_]:=Module[{d=Divisors[n], len}, len=Length[d]; If[OddQ[len], 2*d[[ (len+1)/2]], d[[len/2]]+d[[len/2+1]]]]; msd/@Select[Range[200], CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 09 2018 *)

PROG

(PARI) forcomposite(n=4, 100, d=divisors(n); t=#d; k=if(t%2, 2*d[t\2+1], d[t\2]+d[t\2+1]); print1(k", ")) \\ Charles R Greathouse IV, Jun 08 2016

CROSSREFS

Cf. A002808, A046343, A063655.

Sequence in context: A058979 A225491 A046343 * A319500 A022911 A162310

Adjacent sequences:  A273224 A273225 A273226 * A273228 A273229 A273230

KEYWORD

nonn

AUTHOR

Michel Lagneau, May 18 2016

EXTENSIONS

Name edited by Jon E. Schoenfield, Sep 12 2017

STATUS

approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)