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# User:Oskar Wieland

I'm a software developer based in Munich, Germany

## Pythagoras triangles

Just as shorthand, this is the proposed function:

```int A078644(int64 i)
{
int result = 0; int64 xx = 4*i*i;
for(int64 n=1,x=i+i+1;;n++,x++)
{
xx += x+x-1; if(xx%n) continue;
int64 xn = xx/n; if(xn%2 != n%2) continue;
if((xn-n)/2 > x) result++; else return result;
}
}
```

Here's the formatted code, yz represents the hypotenuse, y and z are the legs:

```int A000005(int64 i)
{
int result = 0; int64 xx = 4*i*i;
for(int64 n=1,x=i+i+1;;n++,x++)
{
xx += x+x-1; if(xx%n) continue;
int64 yz = xx/n; if(yz%2 != n%2) continue;
int64 y = (yz-n)/2, z = (yz+n)/2; if(y <= x) return result;
if(GCD(x,GCD(y,z)) == n) result++;
}
}

int A068068(int64 i)
{
int result = 0; int64 xx = 4*i*i;
for(int64 n=1,x=i+i+1;;n++,x++)
{
xx += x+x-1; if(xx%n) continue;
int64 yz = xx/n; if(yz%2 != n%2) continue;
int64 y = (yz-n)/2, z = (yz+n)/2; if(y <= x) return result;
if(GCD(x,GCD(y,z)) == 1) result++;
}
}
```

```1: (49,1200,1201)
2: (50,624,626)  = 2x (25,312,313)
3: (51,432,435)  = 3x (17,144,145)
4: (52,336,340)  = 4x (13,84,85)
6: (54,240,246)  = 6x (9,40,41)
8: (56,192,200)  = 8x (7,24,25)
9: (57,176,185)
12: (60,144,156) = 12x (5,12,13)
16: (64,120,136) = 8x (8,15,17)
18: (66,112,130) = 2x (33,56,65)
24: (72,96,120)  = 24x (3,4,5)
32: (80,84,116)  = 4x (20,21,29)
A078644(24) = 12, A000005(24) = 8, A068068(24) = 2
```
A068068 -> number of primitive pythagorean triangles (PPT)
1: (49,1200,1201)
9: (57,176,185)
A000005 -> number where the index (difference between hypotenuse and the 2nd leg) and PPT multiplicator are the same
1: (49,1200,1201)
2: (50,624,626) = 2x (25,312,313)
3: (51,432,435) = 3x (17,144,145)
4: (52,336,340) = 4x (13,84,85)
6: (54,240,246) = 6x (9,40,41)
8: (56,192,200) = 8x (7,24,25)
12: (60,144,156) = 12x (5,12,13)
24: (72,96,120) = 24x (3,4,5)
A078644 -> total number of triangles

```1: (51,1300,1301)
2: (52,675,677)
5: (55,300,305)   = 5x (11,60,61)
10: (60,175,185)  = 5x (12,35,37)
25: (75,100,125)  = 25x (3,4,5)
A078644(25) = 5, A000005(25) = 3, A068068(25) = 2
```

```1: (53,1404,1405)