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A049769 Triangular array T read by rows: T(n,k) = (k^3 mod n) + (n^3 mod k).

%I A049769 #12 Sep 08 2022 08:44:58
%S A049769 0,1,0,1,3,0,1,0,4,0,1,4,4,5,0,1,2,3,4,6,0,1,2,7,4,9,7,0,1,0,5,0,7,2,
%T A049769 8,0,1,9,0,2,12,3,2,9,0,1,8,8,4,5,10,9,2,10,0,1,9,7,12,5,12,3,9,11,11,
%U A049769 0,1,8,3,4,8,0,13,8,9,12,12,0
%N A049769 Triangular array T read by rows: T(n,k) = (k^3 mod n) + (n^3 mod k).
%H A049769 G. C. Greubel, <a href="/A049769/b049769.txt">Rows n = 1..100 of triangle, flattened</a>
%F A049769 T(n, k) = A048154(n, k) + A049761(n, k). - _Michel Marcus_, Dec 13 2019
%e A049769 Triangle begins as:
%e A049769   0;
%e A049769   1, 0;
%e A049769   1, 3, 0;
%e A049769   1, 0, 4, 0;
%e A049769   1, 4, 4, 5, 0;
%e A049769   1, 2, 3, 4, 6, 0;
%e A049769   1, 2, 7, 4, 9, 7, 0;
%e A049769   1, 0, 5, 0, 7, 2, 8, 0;
%p A049769 seq(seq( `mod`(k^3, n) + `mod`(n^3, k), k = 1..n), n = 1..15); # _G. C. Greubel_, Dec 13 2019
%t A049769 Table[PowerMod[k,3,n] + PowerMod[n,3,k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Dec 13 2019 *)
%o A049769 (PARI) T(n,k) = lift(Mod(k,n)^3) + lift(Mod(n,k)^3);
%o A049769 for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Dec 13 2019
%o A049769 (Magma) [[Modexp(k,3,n) + Modexp(n,3,k): k in [1..n]]: n in [1..15]]; // _G. C. Greubel_, Dec 13 2019
%o A049769 (Sage) [[power_mod(k,3,n) + power_mod(n,3,k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Dec 13 2019
%o A049769 (GAP) Flat(List([1..15], n-> List([1..n], k-> PowerMod(k,3,n) + PowerMod(n,3,k) ))); # _G. C. Greubel_, Dec 13 2019
%Y A049769 Cf. A048154, A049761, A049767.
%K A049769 nonn,tabl
%O A049769 1,5
%A A049769 _Clark Kimberling_