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A337432 a(n) is the least value of z such that 4/n = 1/x + 1/y + 1/z with 0 < x <= y <= z has at least one solution. 4
2, 3, 3, 10, 6, 14, 6, 9, 10, 33, 9, 52, 14, 12, 12, 102, 18, 57, 15, 21, 22, 138, 18, 50, 26, 27, 21, 232, 24, 248, 24, 33, 34, 30, 27, 370, 38, 39, 30, 164, 35, 258, 33, 36, 46, 329, 36, 98, 50, 51, 39, 742, 54, 44, 42, 57, 58, 885, 45, 549, 62, 56, 48, 60, 66, 603 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

See A073101 and A192787 for the history of the problem, references, and links.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 2..10000, first 576 terms from Robert Israel.

EXAMPLE

a(6)=6 because it is the least denominator z in the A192787(6)=8 solutions

  [x, y, z]: [2, 7, 42], [2, 8, 24], [2, 9, 18], [2, 10, 15], [2, 12, 12],

  [3, 4, 12], [3, 6, 6], [4, 4, 6];

a(13)=52 because the minimum of z in the A192787(13)=4 solutions is 52:

  [4, 18, 468], [4, 20, 130], [4, 26, 52], [5, 10, 130].

MAPLE

f:= proc(n) local z, x, y;

  for z from floor(n/4)+1 do

    for x from floor(n*z/(4*z-n))+1 to z do

      y:= n*x*z/(4*x*z-n*x-n*z);

      if y::posint and y >= x and y <= z then return z fi

  od od

end proc:

map(f, [$2..100]); # Robert Israel, Oct 14 2020

MATHEMATICA

a[n_] := For[z = Floor[n/4] + 1, True, z++, For[x = Floor[n(z/(4z - n))] + 1, x <= z, x++, y = n x z/(4 x z - n x - n z); If[IntegerQ[y] && x <= y <= z, Print[z]; Return [z]]]];

a /@ Range[2, 100] (* Jean-Fran├žois Alcover, Oct 23 2020, after Robert Israel *)

PROG

(PARI) a337432(n)={my(target=4/n, a, b, c, m=oo); for(a=1\target+1, 3\target, my(t=target-1/a); for(b=max(1\t+1, a), 2\t, c=1/(t-1/b); if(denominator(c)==1, m=min(m, max(a, max(b, c)))))); m};

for(k=2, 67, print1(a337432(k), ", "))

CROSSREFS

Cf. A073101, A192787, A292581.

Sequence in context: A194232 A110042 A306101 * A123027 A100652 A094416

Adjacent sequences:  A337429 A337430 A337431 * A337433 A337434 A337435

KEYWORD

nonn,look

AUTHOR

Hugo Pfoertner, Oct 13 2020

STATUS

approved

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Last modified May 11 10:21 EDT 2021. Contains 343788 sequences. (Running on oeis4.)