A164295 Triangle T(n,k) read by rows: sum of the triangles A054521 and A051731.

2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1

Offset: 1

Author

Roger L. Bagula and Mats Granvik, Aug 12 2009

Keywords

• nonn
• tabl

Comments

Zeros in the table, for example T(6,4)=0, indicate that the row and column indices n and k are not coprime and in addition that there is a nonzero remainder n (mod k).

Examples

			The table starts
2
2, 1
2, 1, 1
2, 1, 1, 1
2, 1, 1, 1, 1
2, 1, 1, 0, 1, 1
2, 1, 1, 1, 1, 1, 1
2, 1, 1, 1, 1, 0, 1, 1
2, 1, 1, 1, 1, 0, 1, 1, 1
2, 1, 1, 0, 1, 0, 1, 0, 1, 1
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A054521, A051731.

Programs

Maple

A054521 := proc(n,k) if gcd(n,k) = 1 then 1; else 0 ; fi; end:
A051731 := proc(n,k) if (n mod k) = 0 then 1; else 0 ; fi; end:
A164295 := proc(n,k) A054521(n,k)+A051731(n,k) ; end: seq(seq(A164295(n,k),k=1..n),n=1..10) ;

Mathematica

T[n_, k_] = If[Mod[n, k] == 0, 1, 0] + If[GCD[n, k] == 1, 1, 0];
Table[Table[T[n, k], {k, 1, n}], {n, 1, 10}]; Flatten[%]

Formula

T(n,k) = A054521(n,k) + A051731(n,k), 1<=k<=n, 1<=n.

Extensions

Edited by the Associate Editors of the OEIS, Aug 28 2009