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

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

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			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;
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Crossrefs

Cf. A048154, A049761, A049767.

Programs

GAP

Flat(List([1..15], n-> List([1..n], k-> PowerMod(k,3,n) + PowerMod(n,3,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

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 *)

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

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

Formula

T(n, k) = A048154(n, k) + A049761(n, k). - Michel Marcus, Dec 13 2019