A393614 - OEIS

%I #8 Feb 26 2026 21:48:16

%S 1,26,102,210,984,1218,1295,3355,7644,9282,11130,22148,24024,29997,

%T 47328,48180,54978,69420,91234,92853,151320,170170,193050,208299,

%U 233051,294998,372351,488280,524280,544258,590744,742368,777231,880770,1070745,1196482,1315834,1407770,1766232,1771077,1789320

%N Numbers of the form a*b*c*r/60 where (a,b,c) is a primitive Pythagorean triple with inradius r.

%C Numbers of the form (x - y)^2*(x + y)*x*y^2*(x^2 + y^2)/30 where 1 <= y < x, x and y coprime and one of them even.

%H Robert Israel, <a href="/A393614/b393614.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A393526(n)/60.

%e a(3) = 102 is a term because (with x=4, y=1), the primitive Pythagorean triple (15, 8, 17) has inradius 3 and 15 * 8 * 17 * 3 / 60 = 102.

%p N:= 10^7: # for terms <= N

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

%p for x from 2 while x^6 - x^5 - x^2 + x  <= 30*N do

%p   flag:= false;

%p   for y from 1 to x-1 do

%p     P:= (x - y)^2*(x + y)*x*y^2*(x^2 + y^2)/30;

%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:= (x - y)^2*(x + y)*x*y^2*(x^2 + y^2)/30;

%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, A393526.

%K nonn

%O 1,2

%A _Will Gosnell_ and _Robert Israel_, Feb 23 2026