A393526 Numbers of the form a*b*c*r where (a,b,c) is a primitive Pythagorean triple with inradius r.

60, 1560, 6120, 12600, 59040, 73080, 77700, 201300, 458640, 556920, 667800, 1328880, 1441440, 1799820, 2839680, 2890800, 3298680, 4165200, 5474040, 5571180, 9079200, 10210200, 11583000, 12497940, 13983060, 17699880, 22341060, 29296800, 31456800, 32655480, 35444640, 44542080, 46633860, 52846200

Offset

1,1

Comments

All terms are divisible by 60.

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.

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

N:= 10^8: # for terms <= N
Res:= {}: count:= 0:
for x from 2 while 2*x^6 - 2*x^5 - 2*x^2 + 2*x  <= N do
  flag:= false;
  for y from 1 to x-1 do
    P:= 2*(x - y)^2*(x + y)*x*y^2*(x^2 + y^2);
  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:= 2*(x - y)^2*(x + y)*x*y^2*(x^2 + y^2);
    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

Cf. A393335, A392634, A393614.

Sequence in context: A288960 A269196 A379607 * A054331 A160349 A281373

Adjacent sequences: A393523 A393524 A393525 * A393527 A393528 A393529

Keyword

nonn

Author

Will Gosnell and Robert Israel, Feb 18 2026

Status

approved