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Table of (x+y)/gcd(x,y) where (x,y) runs through the pairs (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...
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%I #15 Oct 26 2019 20:37:46

%S 2,3,3,4,2,4,5,5,5,5,6,3,2,3,6,7,7,7,7,7,7,8,4,8,2,8,4,8,9,9,3,9,9,3,

%T 9,9,10,5,10,5,2,5,10,5,10,11,11,11,11,11,11,11,11,11,11,12,6,4,3,12,

%U 2,12,3,4,6,12,13,13,13,13,13,13,13,13,13,13,13,13,14,7,14,7,14,7,2,7,14,7,14,7,14

%N Table of (x+y)/gcd(x,y) where (x,y) runs through the pairs (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...

%C Can also be viewed as a triangular table T(n,k) (n>=1, 1<=k<=n) read by rows: T(1,1); T(2,1), T(2,2); T(3,1), T(3,2), T(3,3); T(4,1), T(4,2), T(4,3), T(4,4); ... where T(n,k) gives the least value v>0 such that v*k = 0 modulo n+1, i.e., in other words, T(n,k) = (n+1)/gcd(n+1,k).

%F Equals A003057/A003989.

%F T(n, k) = numerator((n+k)/n) = numerator((n+k)/k). - _Michel Marcus_, Dec 29 2013

%e The top left corner of the square array is:

%e 2 3 4 5 6 7 8 9 10 11 ...

%e 3 2 5 3 7 4 9 5 11 ...

%e 4 5 2 7 8 3 10 11 ...

%e 5 3 7 2 9 5 11 ...

%e 6 7 8 9 2 11 ...

%e 7 4 3 5 11 ...

%e 8 9 10 11 ...

%e 9 5 11 ...

%e 10 11 ...

%e 11 ...

%Y GF(2)[X] analog: A106449. Row 1 is n+1, row 2 is LEFT(LEFT(LEFT(A026741))), row 3 is LEFT^4(A051176). Essentially the same as A054531, but without its right-hand edge of all-1's.

%K nonn,tabl

%O 1,1

%A _Antti Karttunen_, May 21 2005