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%I #8 Aug 06 2021 04:49:12
%S 1,2,2,2,4,2,2,5,5,2,2,6,6,6,2,2,7,8,8,7,2,2,8,9,10,9,8,2,2,9,11,12,
%T 12,11,9,2,2,10,12,15,14,15,12,10,2,2,11,14,16,18,18,16,14,11,2,2,12,
%U 15,19,19,22,19,19,15,12,2,2,13,17,21,23,24,24,23,21
%N Array T read by diagonals; T(i,j)=(i+1)*(j+1)-H(i,j), where H is the array in A049615; thus T(i,j) is the number of lattice points in rectangle having diagonal (0,0)-to-(i,j) that are visible from (i,j).
%e Diagonals (each starting on row 0):
%e {1};
%e {2,2};
%e {2,4,2};
%e ...
%e Array begins:
%e 1 2 2 2 2 2 2
%e 2 4 5 6 7 8 9
%e 2 5 6 8 9 11 12
%e 2 6 8 10 12 15 16
%e 2 7 9 12 14 18 19
%e 2 8 11 15 18 22 24
%e 2 9 12 16 19 24 26
%o (PARI) T(n,k) = (n+1)*(k+1) - sum(i=0, n, sum(j=0, k, gcd(i,j)>1));
%o matrix(7,7,n,k, T(n-1,k-1)) \\ _Michel Marcus_, Aug 06 2021
%Y Cf. A049615.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_
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