A054524 Triangle T(n,k): T(n,k) = mu(k) if k divides n, T(n,k)=0 otherwise (n >= 1, 1<=k<=n).

1, 1, -1, 1, 0, -1, 1, -1, 0, 0, 1, 0, 0, 0, -1, 1, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1

Offset: 1

Author

N. J. A. Sloane, Apr 09 2000

Keywords

• sign
• tabl

Crossrefs

Cf. A054521.

Cf. A051731, A128407.

Programs

Mathematica

Clear[t]; t[n_, 1] = 1; t[n_, k_] := t[n, k] = If[k == 1, 1, If[n == k, -Sum[t[n, k - i], {i, 1, k - 1}], If[n > k, t[n - k, k], 0]]]; Flatten[Table[t[n, k], {n, 13}, {k, n}]] (* Mats Granvik, Feb 12 2012 *)
Table[If[Mod[n,k]==0,MoebiusMu[k],0],{n,20},{k,n}]//Flatten (* Harvey P. Dale, Mar 29 2023 *)

Formula

A054524 = A051731 * A128407 - Gary W. Adamson, Mar 02 2007