A228287 - OEIS

%I #17 Aug 08 2023 04:50:00

%S 1,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,2,1,1,2,

%T 1,1,2,1,1,1,2,1,2,1,1,2,3,1,1,1,1,1,2,1,1,1,1,2,3,1,2,3,1,1,1,1,2,1,

%U 2,1,2,1,2,3,1,1,1,1,2,1,1,2,3,1,1,2,1

%N Smallest value of z in the minimal value of x + y*z, given x + y*z = n (where x, y, z are positive integers).

%C If there are multiple triples (x, y, z) for which xy + z = n and x + yz is minimized, consider the triple with smallest z. I.e., this sequence illustrates the smallest z needed to minimize x + yz.

%C For n = 215 the triples (53, 4, 3) and (35, 6, 5) both give the minimal value of x + yz = 65. Thus a(215) = 3.

%p A228287 := proc(n)

%p     local a,x,y,z,zfin ;

%p     a := n+n^2 ;

%p     zfin := n ;

%p     for z from 1 to n-1 do

%p         for x in numtheory[divisors](n-z) do

%p             y := (n-z)/x ;

%p             if x+y*z < a then

%p                 a := x+y*z ;

%p                 zfin := z ;

%p             end if;

%p         end do:

%p     end do:

%p     return zfin;

%p end proc: # _R. J. Mathar_, Sep 02 2013

%t A228287[n_] := Module[{a, x, y, z, zfin}, a = n + n^2; zfin = n; Do[Do[y = (n-z)/x; If[x + y*z < a, a = x + y*z; zfin = z], {x, Divisors[n-z]}], {z, 1, n-1}]; zfin];

%t Table[A228287[n], {n, 2, 100}] (* _Jean-François Alcover_, Aug 08 2023, after _R. J. Mathar_ *)

%Y Cf. A228286.

%K nonn

%O 2,7

%A _Andy Niedermaier_, Aug 19 2013