A125093 Triangle T(n,k) = n*A054525(n,k) read by rows.

1, -2, 2, -3, 0, 3, 0, -4, 0, 4, -5, 0, 0, 0, 5, 6, -6, -6, 0, 0, 6, -7, 0, 0, 0, 0, 0, 7, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, -9, 0, 0, 0, 0, 0, 9, 10, -10, 0, 0, -10, 0, 0, 0, 0, 10, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 12, 0, -12, 0, -12, 0, 0, 0, 0, 0, 12, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 14, -14, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 14, 15, 0, -15, 0

Offset: 1

Author

Gary W. Adamson, Jan 22 2007

Keywords

• tabl
• easy
• sign

Examples

			First few rows of the triangle are:
1;
-2, 2;
-3, 0, 3;
0, -4, 0, 4;
-5, 0, 0, 0, 5;
6, -6, -6, 0, 0, 6;
-7, 0, 0, 0, 0, 0, 7;
...
		

Crossrefs

Cf. A055615, A051731, A127648.

Programs

Maple

A125093 := proc(n,k) if n = k then n; elif n mod k = 0 then n*numtheory[mobius](n/k) ; else 0; end if; end proc:
seq(seq(A125093(n,k),k=1..n),n=1..16) ; # R. J. Mathar, Apr 10 2011

Formula

T(n,1) = n*mu(n) = A055615(n).

Extensions

Offset and definition corrected by R. J. Mathar, Apr 10 2011