A393526 - OEIS

%I #9 Feb 26 2026 21:48:04

%S 60,1560,6120,12600,59040,73080,77700,201300,458640,556920,667800,

%T 1328880,1441440,1799820,2839680,2890800,3298680,4165200,5474040,

%U 5571180,9079200,10210200,11583000,12497940,13983060,17699880,22341060,29296800,31456800,32655480,35444640,44542080,46633860,52846200

%N Numbers of the form a*b*c*r where (a,b,c) is a primitive Pythagorean triple with inradius r.

%C All terms are divisible by 60.

%C Numbers of the form 2*(x - y)^2*(x + y)*x*y^2*(x^2 + y^2) where 1 <= y < x, x and y coprime and one of them even.

%C Are there any terms that correspond to more than one (x,y)?

%H Robert Israel, <a href="/A393526/b393526.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 6120 is a term because (with x=4, y=1), the primitive Pythagorean triple (15, 8, 17) has inradius 3 and 15 * 8 * 17 * 3 = 6120.

%p N:= 10^8: # for terms <= N

%p Res:= {}: count:= 0:

%p for x from 2 while 2*x^6 - 2*x^5 - 2*x^2 + 2*x  <= N do

%p   flag:= false;

%p   for y from 1 to x-1 do

%p     P:= 2*(x - y)^2*(x + y)*x*y^2*(x^2 + y^2);

%p   if P > N then flag:= true; y1:= y; break fi;

%p     if igcd(x, y) = 1 and (x+y)::odd  then

%p       count:= count+1; Res:= Res union {P};

%p     fi

%p   od;

%p   if flag then

%p     for y from x-1 to y1+1 by -1 do

%p     P:= 2*(x - y)^2*(x + y)*x*y^2*(x^2 + y^2);

%p     if P > N then break fi;

%p       if igcd(x, y) = 1 and (x+y)::odd  then

%p          count:= count+1; Res:= Res union {P};

%p     fi od fi

%p od:

%p sort(convert(Res, list));

%Y Cf. A393335, A392634, A393614.

%K nonn

%O 1,1

%A _Will Gosnell_ and _Robert Israel_, Feb 18 2026