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A049769
Triangular array T read by rows: T(n,k) = (k^3 mod n) + (n^3 mod k).
2
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, 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, 0, 1, 8, 3, 4, 8, 0, 13, 8, 9, 12, 12, 0
OFFSET
1,5
FORMULA
T(n, k) = A048154(n, k) + A049761(n, k). - Michel Marcus, Dec 13 2019
EXAMPLE
Triangle begins as:
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, 8, 0;
MAPLE
seq(seq( `mod`(k^3, n) + `mod`(n^3, k), k = 1..n), n = 1..15); # G. C. Greubel, Dec 13 2019
MATHEMATICA
Table[PowerMod[k, 3, n] + PowerMod[n, 3, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Dec 13 2019 *)
PROG
(PARI) T(n, k) = lift(Mod(k, n)^3) + lift(Mod(n, k)^3);
for(n=1, 15, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Dec 13 2019
(Magma) [[Modexp(k, 3, n) + Modexp(n, 3, k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019
(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
(GAP) Flat(List([1..15], n-> List([1..n], k-> PowerMod(k, 3, n) + PowerMod(n, 3, k) ))); # G. C. Greubel, Dec 13 2019
CROSSREFS
KEYWORD
nonn,tabl
STATUS
approved