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A049767 Triangular array T, read by rows: T(n,k) = (k^2 mod n) + (n^2 mod k), for k = 1..n and n >= 1.

%I A049767 #21 Sep 08 2022 08:44:58
%S A049767 0,1,0,1,2,0,1,0,2,0,1,5,5,2,0,1,4,3,4,2,0,1,5,3,3,8,2,0,1,4,2,0,5,8,
%T A049767 2,0,1,5,0,8,8,3,8,2,0,1,4,10,6,5,10,11,8,2,0,1,5,10,6,4,4,7,10,8,2,0,
%U A049767 1,4,9,4,5,0,5,4,9,8,2,0,1,5,10,4
%N A049767 Triangular array T, read by rows: T(n,k) = (k^2 mod n) + (n^2 mod k), for k = 1..n and n >= 1.
%H A049767 G. C. Greubel, <a href="/A049767/b049767.txt">Rows n = 1..100 of triangle, flattened</a>
%F A049767 T(n, k) = A048152(n, k) + A049759(n, k). - _Michel Marcus_, Nov 21 2019
%e A049767 Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
%e A049767   0;
%e A049767   1,  0;
%e A049767   1,  2,  0;
%e A049767   1,  0,  2,  0;
%e A049767   1,  5,  5,  2,  0;
%e A049767   1,  4,  3,  4,  2,  0;
%e A049767   1,  5,  3,  3,  8,  2,  0;
%e A049767   1,  4,  2,  0,  5,  8,  2,  0;
%e A049767   1,  5,  0,  8,  8,  3,  8,  2,  0;
%e A049767   1,  4, 10,  6,  5, 10, 11,  8,  2,  0;
%e A049767   ...
%p A049767 seq(seq( `mod`(k^2, n) + `mod`(n^2, k), k = 1..n), n = 1..15); # _G. C. Greubel_, Dec 13 2019
%t A049767 Table[PowerMod[k,2,n] + PowerMod[n,2,k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Dec 13 2019 *)
%o A049767 (PARI) T(n,k) = lift(Mod(k,n)^2) + lift(Mod(n,k)^2);
%o A049767 for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Dec 13 2019
%o A049767 (Magma) [[Modexp(k,2,n) + Modexp(n,2,k): k in [1..n]]: n in [1..15]]; // _G. C. Greubel_, Dec 13 2019
%o A049767 (Sage) [[power_mod(k,2,n) + power_mod(n,2,k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Dec 13 2019
%o A049767 (GAP) Flat(List([1..15], n-> List([1..n], k-> PowerMod(k,2,n) + PowerMod(n,2,k) ))); # _G. C. Greubel_, Dec 13 2019
%Y A049767 Row sums are in A049768.
%Y A049767 Cf. A048152, A049759.
%K A049767 nonn,tabl
%O A049767 1,5
%A A049767 _Clark Kimberling_