A191907 Square array read by antidiagonals up: T(n,k) = -(n-1) if n divides k, else 1.

0, 1, 0, 1, -1, 0, 1, 1, 1, 0, 1, 1, -2, -1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, -3, 1, -1, 0, 1, 1, 1, 1, 1, -2, 1, 0, 1, 1, 1, 1, -4, 1, 1, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, -5, 1, -3, -2, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, -6, 1, 1, 1, 1, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, 1, -2, 1, 0, 1, 1, 1, 1, 1, 1, 1, -7, 1, 1, 1, -3, 1, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0

Offset: 1

Author

Mats Granvik, Jun 19 2011

Keywords

• sign
• tabl

Comments

Apart from the top row, the same as A177121.

Sum_{k>=1} T(n,k)/k = log(n); this has been pointed out by Jaume Oliver Lafont in A061347 and A002162.

Examples

			Table starts:
0..0..0..0..0..0..0..0..0...
1.-1..1.-1..1.-1..1.-1..1...
1..1.-2..1..1.-2..1..1.-2...
1..1..1.-3..1..1..1.-3..1...
1..1..1..1.-4..1..1..1..1...
1..1..1..1..1.-5..1..1..1...
1..1..1..1..1..1.-6..1..1...
1..1..1..1..1..1..1.-7..1...
1..1..1..1..1..1..1..1.-8...
		

Crossrefs

Cf. A002162, A002391, A016627, A191904.

Programs

Mathematica

Clear[t, n, k];
nn = 30;
t[n_, k_] := t[n, k] = If[Mod[n, k] == 0, -(k - 1), 1]
MatrixForm[Transpose[Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]]]

PARI

N=20; M=matrix(N,N,n,k, if(n%k==0,1-k,1))~

Formula

If n divides k then T(n,k) = -(n-1) else 1.