OFFSET
1,2
COMMENTS
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.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A393526(n)/60.
EXAMPLE
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.
MAPLE
N:= 10^7: # for terms <= N
Res:= {}: count:= 0:
for x from 2 while x^6 - x^5 - x^2 + x <= 30*N do
flag:= false;
for y from 1 to x-1 do
P:= (x - y)^2*(x + y)*x*y^2*(x^2 + y^2)/30;
if P > N then flag:= true; y1:= y; break fi;
if igcd(x, y) = 1 and (x+y)::odd then
count:= count+1; Res:= Res union {P};
fi
od;
if flag then
for y from x-1 to y1+1 by -1 do
P:= (x - y)^2*(x + y)*x*y^2*(x^2 + y^2)/30;
if P > N then break fi;
if igcd(x, y) = 1 and (x+y)::odd then
count:= count+1; Res:= Res union {P};
fi od fi
od:
sort(convert(Res, list));
CROSSREFS
KEYWORD
nonn
AUTHOR
Will Gosnell and Robert Israel, Feb 23 2026
STATUS
approved