A295782 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the number of coprime pairs (a,b) with -n <= a <= n, -k <= b <= k.
8, 12, 12, 16, 16, 16, 20, 24, 24, 20, 24, 28, 32, 28, 24, 28, 36, 40, 40, 36, 28, 32, 40, 52, 48, 52, 40, 32, 36, 48, 56, 64, 64, 56, 48, 36, 40, 52, 68, 68, 80, 68, 68, 52, 40, 44, 60, 76, 84, 88, 88, 84, 76, 60, 44, 48, 64, 84, 92, 108, 96, 108, 92, 84, 64, 48
Offset: 1
Examples
A(2,1)=12 because there are twelve coprime pairs (1,0), (2,1), (1,1), (0,1), (-1,1), (-2,1), (-1,0), (-2,-1), (-1,-1), (0,-1), (1,-1), (2,-1).
Square array begins:
8, 12, 16, 20, 24, 28, 32, ...
12, 16, 24, 28, 36, 40, 48, ...
16, 24, 32, 40, 52, 56, 68, ...
20, 28, 40, 48, 64, 68, 84, ...
24, 36, 52, 64, 80, 88, 108, ...
28, 40, 56, 68, 88, 96, 120, ...
32, 48, 68, 84, 108, 120, 144, ...
36, 52, 76, 92, 120, 132, 160, ...
Links
- Seiichi Manyama, Antidiagonals n = 1..140, flattened
- Wikipedia, Coprime integers
Formula
A(n,k) = A(k,n).