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A049765 Triangular array T, read by rows: T(n,k) = (k mod n) + (n mod k), for k = 1..n and n >= 1.

%I A049765 #20 Sep 08 2022 08:44:58
%S A049765 0,1,0,1,3,0,1,2,4,0,1,3,5,5,0,1,2,3,6,6,0,1,3,4,7,7,7,0,1,2,5,4,8,8,
%T A049765 8,0,1,3,3,5,9,9,9,9,0,1,2,4,6,5,10,10,10,10,0,1,3,5,7,6,11,11,11,11,
%U A049765 11,0,1,2,3,4,7,6,12,12,12,12,12,0
%N A049765 Triangular array T, read by rows: T(n,k) = (k mod n) + (n mod k), for k = 1..n and n >= 1.
%H A049765 G. C. Greubel, <a href="/A049765/b049765.txt">Rows n = 1..100 of triangle, flattened</a>
%e A049765 Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
%e A049765   0;
%e A049765   1, 0;
%e A049765   1, 3, 0;
%e A049765   1, 2, 4, 0;
%e A049765   1, 3, 5, 5, 0;
%e A049765   1, 2, 3, 6, 6,  0;
%e A049765   1, 3, 4, 7, 7,  7,  0;
%e A049765   1, 2, 5, 4, 8,  8,  8,  0;
%e A049765   1, 3, 3, 5, 9,  9,  9,  9,  0;
%e A049765   1, 2, 4, 6, 5, 10, 10, 10, 10, 0;
%e A049765   ...
%p A049765 seq(seq( `mod`(k, n) + `mod`(n, k), k = 1..n), n = 1..15); # _G. C. Greubel_, Dec 13 2019
%t A049765 Table[Mod[k,n] + Mod[n,k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Dec 13 2019 *)
%o A049765 (PARI) T(n,k) = k%n + n%k;
%o A049765 for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Dec 13 2019
%o A049765 (Magma) [[(k mod n) + (n mod k): k in [1..n]]: n in [1..15]]; // _G. C. Greubel_, Dec 13 2019
%o A049765 (Sage) [[(k%n) + (n%k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Dec 13 2019
%o A049765 (GAP) Flat(List([1..15], n-> List([1..n], k-> (k mod n) + (n mod k) ))); # _G. C. Greubel_, Dec 13 2019
%Y A049765 Row sums are in A049766.
%Y A049765 Cf. A048158, A049767, A049768.
%K A049765 nonn,tabl
%O A049765 1,5
%A A049765 _Clark Kimberling_