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A049761 Triangular array T, read by rows: T(n,k) = n^3 mod k, for k = 1..n and n >= 1.

%I A049761 #18 Sep 08 2022 08:44:58
%S A049761 0,0,0,0,1,0,0,0,1,0,0,1,2,1,0,0,0,0,0,1,0,0,1,1,3,3,1,0,0,0,2,0,2,2,
%T A049761 1,0,0,1,0,1,4,3,1,1,0,0,0,1,0,0,4,6,0,1,0,0,1,2,3,1,5,1,3,8,1,0,0,0,
%U A049761 0,0,3,0,6,0,0,8,1,0,0,1,1,1,2,1,6,5,1,7,8,1,0
%N A049761 Triangular array T, read by rows: T(n,k) = n^3 mod k, for k = 1..n and n >= 1.
%H A049761 G. C. Greubel, <a href="/A049761/b049761.txt">Rows n = 1..100 of triangle, flattened</a>
%e A049761 Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
%e A049761   0;
%e A049761   0, 0;
%e A049761   0, 1, 0;
%e A049761   0, 0, 1, 0;
%e A049761   0, 1, 2, 1, 0;
%e A049761   0, 0, 0, 0, 1, 0;
%e A049761   0, 1, 1, 3, 3, 1, 0;
%e A049761   0, 0, 2, 0, 2, 2, 1, 0;
%e A049761   0, 1, 0, 1, 4, 3, 1, 1, 0;
%e A049761   0, 0, 1, 0, 0, 4, 6, 0, 1, 0;
%e A049761   0, 1, 2, 3, 1, 5, 1, 3, 8, 1, 0;
%e A049761   ...
%p A049761 seq(seq( `mod`(n^3, k), k = 1..n), n = 1..15); # _G. C. Greubel_, Dec 13 2019
%t A049761 Table[PowerMod[n,3,k], {n,15}, {k, n}]//Flatten (* _G. C. Greubel_, Dec 13 2019 *)
%o A049761 (PARI) T(n,k) = lift(Mod(n,k)^3);
%o A049761 for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Dec 13 2019
%o A049761 (Magma) [[Modexp(n,3,k): k in [1..n]]: n in [1..15]]; // _G. C. Greubel_, Dec 13 2019
%o A049761 (Sage) [[power_mod(n,3,k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Dec 13 2019
%o A049761 (GAP) Flat(List([1..15], n-> List([1..n], k-> PowerMod(n,3,k) ))); # _G. C. Greubel_, Dec 13 2019
%Y A049761 Row sums are in A049762.
%Y A049761 Cf. A049759, A049760, A049763, A049764.
%K A049761 nonn,tabl
%O A049761 1,13
%A A049761 _Clark Kimberling_