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Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.
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%I #16 Feb 17 2021 13:32:06

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

%C We define gcd(0,0) = 0.

%C This sequence arose when studying Reed Kelly's A214551.

%e The array begins:

%e 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...

%e 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, ...

%e 1, 4, 5, 2, 7, 8, 3, 10, 11, 4, 13, 14, 5, ...

%e 1, 5, 3, 7, 2, 9, 5, 11, 3, 13, 7, 15, 4, ...

%e 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, ...

%e 1, 7, 4, 3, 5, 11, 2, 13, 7, 5, 8, 17, 3, ...

%e 1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 17, 18, 19, ...

%e 1, 9, 5, 11, 3, 13, 7, 15, 2, 17, 9, 19, 5, ...

%e 1, 10, 11, 4, 13, 14, 5, 16, 17, 2, 19, 20, 7, ...

%e 1, 11, 6, 13, 7, 3, 8, 17, 9, 19, 2, 21, 11, ...

%e 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 23, ...

%e 1, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 2, ...

%e ...

%e The first few antidiagonals are:

%e [0]

%e [1, 1]

%e [1, 2, 1]

%e [1, 3, 3, 1]

%e [1, 4, 2, 4, 1]

%e [1, 5, 5, 5, 5, 1]

%e [1, 6, 3, 2, 3, 6, 1]

%e [1, 7, 7, 7, 7, 7, 7, 1]

%e [1, 8, 4, 8, 2, 8, 4, 8, 1]

%e ...

%p fa:= (m,n) -> if m=0 and n=0 then 0 else (m+n)/igcd(m,n); fi;

%p for m from 0 to 12 do lprint([seq(fa(m-n,n),n=0..m)]); od:

%p for m from 0 to 12 do lprint([seq(fa(m,n),n=0..12)]); od:

%Y A054531 is a similar sequence. See also A341315, A341316.

%Y Cf. A214551.

%K nonn,tabl

%O 0,5

%A _N. J. A. Sloane_, Feb 17 2021