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A337942 Table read by antidiagonals: T(n, k) is the least positive m such that (m*n) mod k = (m*k) mod n, with n > 0 and k > 0.

%I A337942 #8 Oct 08 2020 03:38:20
%S A337942 1,2,2,3,1,3,4,5,5,4,5,2,1,2,5,6,3,2,2,3,6,7,3,2,1,2,3,7,8,11,2,7,7,2,
%T A337942 11,8,9,4,17,5,1,5,17,4,9,10,5,11,13,3,3,13,11,5,10,11,5,3,2,3,1,3,2,
%U A337942 3,5,11,12,17,7,3,28,10,10,28,3,7,17,12
%N A337942 Table read by antidiagonals: T(n, k) is the least positive m such that (m*n) mod k = (m*k) mod n, with n > 0 and k > 0.
%H A337942 Rémy Sigrist, <a href="/A337942/a337942.png">Scatterplot of (x, y) such that T(x, y) is even and 1 <= x, y, <= 1000</a>
%H A337942 Rémy Sigrist, <a href="/A337942/a337942_1.png">Scatterplot of (x, y) such that T(x, y) divides x*y and 1 <= x, y, <= 1000</a>
%F A337942 T(n, k) = T(k, n) <= k*n.
%F A337942 T(n, n) = 1.
%F A337942 T(n, 1) = n.
%F A337942 T(n, n^2) = n.
%F A337942 T(n, n^3) = n^2.
%F A337942 T(n, n^k) = n^(k-1) for any k > 0.
%F A337942 T(n, n+1) = A123684(n+1) for any n > 2.
%e A337942 Array T(n, k) begins:
%e A337942   n\k|  1   2   3   4   5   6   7   8   9  10
%e A337942   ---+---------------------------------------
%e A337942     1|  1   2   3   4   5   6   7   8   9  10
%e A337942     2|  2   1   5   2   3   3  11   4   5   5
%e A337942     3|  3   5   1   2   2   2  17  11   3   7
%e A337942     4|  4   2   2   1   7   5  13   2   3   3
%e A337942     5|  5   3   2   7   1   3   3  28  13   2
%e A337942     6|  6   3   2   5   3   1  10   2   5   2
%e A337942     7|  7  11  17  13   3  10   1   4   4  25
%e A337942     8|  8   4  11   2  28   2   4   1  13   7
%e A337942     9|  9   5   3   3  13   5   4  13   1   5
%e A337942    10| 10   5   7   3   2   2  25   7   5   1
%o A337942 (PARI) T(n,k) = for (m=1, oo, if ((m*n)%k==(m*k)%n, return (m)))
%Y A337942 Cf. A123684.
%K A337942 nonn,tabl
%O A337942 1,2
%A A337942 _Rémy Sigrist_, Oct 01 2020