A143256 Triangle read by rows, matrix multiplication A051731 * A128407 * A127648, 1<=k<=n.

1, 1, -2, 1, 0, -3, 1, -2, 0, 0, 1, 0, 0, 0, -5, 1, -2, -3, 0, 0, 6, 1, 0, 0, 0, 0, 0, -7, 1, -2, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -5, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 1, -2, -3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 1, -2, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 14

Offset: 1

Author

Gary W. Adamson, Aug 02 2008

Keywords

• tabl
• sign

Comments

Right border = n*mu(n) = A055615.

Row sums = A023900: (1, -1, -2, -1, -4, 2, -6,...).

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..9870

Crossrefs

Cf. A008683, A055615, A051731, A128407, A127648, A023900.

Programs

Maple

seq(seq(`if`(i mod j = 0, j*numtheory:-mobius(j),0), j=1..i),i=1..20); # Robert Israel, Sep 07 2014

Mathematica

Table[If[Divisible[n, k], k MoebiusMu[k], 0], {n, 1, 14}, {k, 1, n}] (* Jean-François Alcover, Jun 19 2019 *)

Sage

A143256_row = lambda n: [k*moebius(k) if k.divides(n) else 0 for k in (1..n)]
for n in (1..10): print(A143256_row(n)) # Peter Luschny, Jan 05 2018

Formula

Triangle read by rows, A051731 * A128407 * A127648, 1<=k<=n