A046805 If n=sum a_i b_i, (a_i,b_i positive integers) then a(n)=max value of min(all a_i and b_i).

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 2, 2, 3, 4, 2, 3, 2, 4, 3, 2, 2, 4, 5, 2, 3, 4, 3, 5, 3, 4, 3, 3, 5, 6, 3, 3, 3, 5, 4, 6, 3, 4, 5, 4, 3, 6, 7, 5, 4, 4, 4, 6, 5, 7, 4, 4, 4, 6, 5, 4, 7, 8, 5, 6, 5, 4, 4, 7, 5, 8, 5, 5, 5, 5, 7, 6, 5, 8, 9, 5, 5, 7, 6, 5, 5, 8, 5, 9, 7, 6, 5, 5, 5, 8, 6, 7, 9, 10, 5, 6, 6, 8

Offset

1,4

Comments

From Robert Israel, Aug 29 2018: (Start)

a(n) <= sqrt(n), with equality if n is a square.

a(n) >= A033676(n).

a(m+n) >= min(a(m), a(n)). (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(13)=2 since 13=2*2+3*3.

Maple

A046805 := proc(n)
    local p, a, abmin, divmin;
    a := 0 ;
    for p in combinat[partition](n) do
        abmin := 1+n ;
        for abprod in p do
            divmin := A033676(abprod) ;
            abmin := min(abmin, divmin) ;
        end do:
        a := max(a, abmin) ;
    end do:
    a ;
end proc: # R. J. Mathar, Oct 12 2015
# alternative program:
f:= proc(n) option remember; local v, a, b, vmax;
  if issqr(n) then return sqrt(n) fi;
  vmax:= 1;
  for a from floor(sqrt(n)) by -1 while a > vmax do
    for b from a to n/a do
      v:= min(a, procname(n - a*b));
      vmax:= max(vmax, v);
  od od;
  vmax
end proc:
f(0):= infinity:
map(f, [$1..200]); # Robert Israel, Aug 29 2018

Mathematica

f[n_] := f[n] = Module[{v, a, b, vMax}, If[IntegerQ[Sqrt[n]], Return[ Sqrt[n]]]; vMax = 1; For[a = Floor[Sqrt[n]], a > vMax, a--, For[b = a, b <= n/a, b++, v = Min[a, f[n - a b]]; vMax = Max[vMax, v]]]; vMax];
f[0] = Infinity;
Array[f, 200] (* Jean-François Alcover, Jun 23 2020, after Robert Israel *)

Crossrefs

Cf. A033676.

Sequence in context: A033676 A095165 A355366 * A034880 A257977 A070966

Adjacent sequences: A046802 A046803 A046804 * A046806 A046807 A046808

Keyword

easy,nice,nonn,look

Author

Erich Friedman

Status

approved