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%I #8 Sep 26 2022 10:39:11
%S 2,3,3,4,1,4,5,5,5,5,6,3,2,3,6,7,7,7,7,7,7,8,2,8,1,8,2,8,9,9,1,9,9,1,
%T 9,9,10,5,10,5,2,5,10,5,10,11,11,11,11,11,11,11,11,11,11,12,3,4,3,12,
%U 1,12,3,4,3,12,13,13,13,13,13,13,13,13,13,13,13,13
%N Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the numerator of 1/n + 1/k.
%C See A257522 for the corresponding denominators.
%H Rémy Sigrist, <a href="/A357372/b357372.txt">Table of n, a(n) for n = 1..10011</a>
%F A(n, k) = (n + k) / gcd(n + k, n*k).
%F A(n, k) = A(k, n).
%F A(n, 1) = n + 1.
%F A(n, n) = A000034(n).
%F A(n, n+1) = 2*n + 1.
%e Array A(n, k) begins:
%e n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13
%e ----+---------------------------------------------------
%e 1 | 2 3 4 5 6 7 8 9 10 11 12 13 14
%e 2 | 3 1 5 3 7 2 9 5 11 3 13 7 15
%e 3 | 4 5 2 7 8 1 10 11 4 13 14 5 16
%e 4 | 5 3 7 1 9 5 11 3 13 7 15 1 17
%e 5 | 6 7 8 9 2 11 12 13 14 3 16 17 18
%e 6 | 7 2 1 5 11 1 13 7 5 4 17 1 19
%e 7 | 8 9 10 11 12 13 2 15 16 17 18 19 20
%e 8 | 9 5 11 3 13 7 15 1 17 9 19 5 21
%e 9 | 10 11 4 13 14 5 16 17 2 19 20 7 22
%e 10 | 11 3 13 7 3 4 17 9 19 1 21 11 23
%e 11 | 12 13 14 15 16 17 18 19 20 21 2 23 24
%e 12 | 13 7 5 1 17 1 19 5 7 11 23 1 25
%e 13 | 14 15 16 17 18 19 20 21 22 23 24 25 2
%t Flatten[Table[Numerator[1/i + 1/(m - i)], {m, 13}, {i, m - 1}]]
%o (PARI) A(n,k) = numerator(1/n + 1/k)
%Y Cf. A000034, A257522.
%K nonn,tabl,easy,frac
%O 1,1
%A _Rémy Sigrist_, Sep 25 2022