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

Author

Seiichi Manyama, Nov 27 2017

Keywords

• nonn
• tabl

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

Crossrefs

For n > 0, columns k = 2,3 give A295821, A295822.

Main diagonal gives A137243.

Formula

A(n,k) = A(k,n).