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A102495 Integers n such that there exist integers x,y,z from {1,2,...,n-1} for which x*y*z = (n-x)*(n-y)*(n-z) and the factors x, y, z are all different from any of n-x, n-y, n-z (this is always the case for odd n; and x,y,z must differ from n/2 for even n). 3
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-Fran├žois Alcover, Jun 16 2020 *)

CROSSREFS

Cf. A102505, A102509.

Sequence in context: A134617 A113529 A214410 * A133288 A322710 A316743

Adjacent sequences:  A102492 A102493 A102494 * A102496 A102497 A102498

KEYWORD

nonn

AUTHOR

Max Alekseyev, Feb 26 2005

STATUS

approved

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Last modified July 7 16:09 EDT 2020. Contains 335496 sequences. (Running on oeis4.)