A102495 - OEIS

A102495

Integers k such that there exist integers x,y,z from {1,2,...,k-1} for which x*y*z = (k-x)*(k-y)*(k-z) and the factors x, y, z are all different from any of k-x, k-y, k-z (this is always the case for odd k; and x,y,z must differ from k/2 for even k).

15, 20, 24, 30, 35, 40, 42, 45, 48, 55, 56, 60, 63, 65, 66, 70, 72, 75, 77, 78, 80, 84, 85, 88, 90, 91, 96, 99, 100, 104, 105, 110, 112, 117, 119, 120, 126, 130, 132, 135, 136, 140, 143, 144, 150, 152, 153, 154, 156, 160, 161, 165, 168, 170, 171, 175

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

OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..3500

MAPLE

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

for x from 1 to n-1 do

for y from x to n-1 do

z:= (n-x)*(n-y)*n/(n^2-n*x-n*y+2*x*y);

if z::integer and not has({x, y, z}, n/2) then return true fi;

od od;

false

end proc:

select(Filter, [$1..300]); # Robert Israel, Dec 30 2015

MATHEMATICA

okQ[n_] := Do[z = (n-x)(n-y)n/(n^2 - n x - n y + 2 x y); If[IntegerQ[z] && AllTrue[{x, y, z}, FreeQ[#, (n-x)|(n-y)|(n-z)]&], Return[True]], {x, 1, n-1}, {y, x, n-1}];

Select[Range[200], okQ] (* Jean-François Alcover, Jun 16 2020 *)

CROSSREFS

Cf. A102505, A102509.

Sequence in context: A373138 A113529 A214410 * A133288 A322710 A316743

Adjacent sequences: A102492 A102493 A102494 * A102496 A102497 A102498

KEYWORD

nonn

AUTHOR

Max Alekseyev, Feb 26 2005

STATUS

approved