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A341314 Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.

%I A341314 #16 Feb 17 2021 13:32:06
%S A341314 0,1,1,1,2,1,1,3,3,1,1,4,2,4,1,1,5,5,5,5,1,1,6,3,2,3,6,1,1,7,7,7,7,7,
%T A341314 7,1,1,8,4,8,2,8,4,8,1,1,9,9,3,9,9,3,9,9,1,1,10,5,10,5,2,5,10,5,10,1,
%U A341314 1,11,11,11,11,11,11,11,11,11,11,1,1,12,6,4,3,12,2,12,3,4,6,12,1
%N A341314 Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.
%C A341314 We define gcd(0,0) = 0.
%C A341314 This sequence arose when studying Reed Kelly's A214551.
%e A341314 The array begins:
%e A341314   0,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
%e A341314   1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
%e A341314   1,  3,  2,  5,  3,  7,  4,  9,  5, 11,  6, 13,  7, ...
%e A341314   1,  4,  5,  2,  7,  8,  3, 10, 11,  4, 13, 14,  5, ...
%e A341314   1,  5,  3,  7,  2,  9,  5, 11,  3, 13,  7, 15,  4, ...
%e A341314   1,  6,  7,  8,  9,  2, 11, 12, 13, 14,  3, 16, 17, ...
%e A341314   1,  7,  4,  3,  5, 11,  2, 13,  7,  5,  8, 17,  3, ...
%e A341314   1,  8,  9, 10, 11, 12, 13,  2, 15, 16, 17, 18, 19, ...
%e A341314   1,  9,  5, 11,  3, 13,  7, 15,  2, 17,  9, 19,  5, ...
%e A341314   1, 10, 11,  4, 13, 14,  5, 16, 17,  2, 19, 20,  7, ...
%e A341314   1, 11,  6, 13,  7,  3,  8, 17,  9, 19,  2, 21, 11, ...
%e A341314   1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,  2, 23, ...
%e A341314   1, 13,  7,  5,  4, 17,  3, 19,  5,  7, 11, 23,  2, ...
%e A341314 ...
%e A341314 The first few antidiagonals are:
%e A341314   [0]
%e A341314   [1, 1]
%e A341314   [1, 2, 1]
%e A341314   [1, 3, 3, 1]
%e A341314   [1, 4, 2, 4, 1]
%e A341314   [1, 5, 5, 5, 5, 1]
%e A341314   [1, 6, 3, 2, 3, 6, 1]
%e A341314   [1, 7, 7, 7, 7, 7, 7, 1]
%e A341314   [1, 8, 4, 8, 2, 8, 4, 8, 1]
%e A341314   ...
%p A341314 fa:= (m,n) -> if m=0 and n=0 then 0 else (m+n)/igcd(m,n); fi;
%p A341314 for m from 0 to 12 do lprint([seq(fa(m-n,n),n=0..m)]); od:
%p A341314 for m from 0 to 12 do lprint([seq(fa(m,n),n=0..12)]); od:
%Y A341314 A054531 is a similar sequence.  See also A341315, A341316.
%Y A341314 Cf. A214551.
%K A341314 nonn,tabl
%O A341314 0,5
%A A341314 _N. J. A. Sloane_, Feb 17 2021