A106478 Inverse of sequence array for Euler phi function.

1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 3, -1, 1, -1, -1, 1, -3, 3, -1, 1, -1, -1, 1, -1, -3, 3, -1, 1, -1, -1, 1, 7, -1, -3, 3, -1, 1, -1, -1, 1, -9, 7, -1, -3, 3, -1, 1, -1, -1, 1, 5, -9, 7, -1, -3, 3, -1, 1, -1, -1, 1, -1, 5, -9, 7, -1, -3, 3, -1, 1, -1, -1, 1, -7, -1, 5, -9, 7, -1, -3, 3, -1, 1, -1, -1, 1, 25, -7, -1, 5, -9, 7, -1, -3, 3, -1, 1, -1, -1, 1

Offset: 0

Author

Paul Barry, May 03 2005

Keywords

• easy
• sign
• tabl

Comments

Row sums are A106480. Sequence matrix for A106479.

Examples

			Triangle begins:
   1;
  -1,  1;
   1, -1, -1,  1;
  -1,  1, -1, -1,  1;
   3, -1,  1, -1, -1,  1;
  -3,  3, -1,  1, -1, -1,  1;
  -1, -3,  3, -1,  1, -1, -1, 1;
   ...
		

Crossrefs

Cf. A000010 (phi), A106476, A106477, A106479, A106480.

Programs

Mathematica

T[n_, k_] := If[k <= n, EulerPhi[n - k + 1], 0]; With[{max = 14}, Tinv = Inverse[Table[T[n, k], {n, 0, max - 1}, {k, 0, max - 1}]]; Table[Tinv[[n, k]], {n, 1, max}, {k, 1, n}] // Flatten] (* Amiram Eldar, Nov 16 2024 *)

Formula

Riordan array (1/Sum_{j>=0}, phi(j+1) x^j, x).