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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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

CROSSREFS

Cf. A033676.

Sequence in context: A059981 A033676 A095165 * A034880 A257977 A070966

Adjacent sequences:  A046802 A046803 A046804 * A046806 A046807 A046808

KEYWORD

easy,nice,nonn,look

AUTHOR

Erich Friedman

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)