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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.

%I A295782 #27 Nov 29 2017 17:00:02
%S A295782 8,12,12,16,16,16,20,24,24,20,24,28,32,28,24,28,36,40,40,36,28,32,40,
%T A295782 52,48,52,40,32,36,48,56,64,64,56,48,36,40,52,68,68,80,68,68,52,40,44,
%U A295782 60,76,84,88,88,84,76,60,44,48,64,84,92,108,96,108,92,84,64,48
%N 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.
%H A295782 Seiichi Manyama, <a href="/A295782/b295782.txt">Antidiagonals n = 1..140, flattened</a>
%H A295782 Wikipedia, <a href="http://en.wikipedia.org/wiki/Coprime_integers">Coprime integers</a>
%F A295782 A(n,k) = A(k,n).
%e A295782 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).
%e A295782 Square array begins:
%e A295782     8, 12, 16, 20,  24,  28,  32, ...
%e A295782    12, 16, 24, 28,  36,  40,  48, ...
%e A295782    16, 24, 32, 40,  52,  56,  68, ...
%e A295782    20, 28, 40, 48,  64,  68,  84, ...
%e A295782    24, 36, 52, 64,  80,  88, 108, ...
%e A295782    28, 40, 56, 68,  88,  96, 120, ...
%e A295782    32, 48, 68, 84, 108, 120, 144, ...
%e A295782    36, 52, 76, 92, 120, 132, 160, ...
%Y A295782 For n > 0, columns k = 2,3 give A295821, A295822.
%Y A295782 Main diagonal gives A137243.
%K A295782 nonn,tabl
%O A295782 1,1
%A A295782 _Seiichi Manyama_, Nov 27 2017