A129691 Inverse of A054523.

1, -1, 1, -2, 0, 1, -1, -1, 0, 1, -4, 0, 0, 0, 1, 2, -2, -1, 0, 0, 1, -6, 0, 0, 0, 0, 0, 1, -1, -1, 0, -1, 0, 0, 0, 1, -2, 0, -2, 0, 0, 0, 0, 0, 1, 4, -4, 0, 0, -1, 0, 0, 0, 0, 1, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, -1, -2, 0, -1, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, May 04 2007

Keywords

• tabl
• sign

Comments

Row sums = A130054, (1, -1, -1, -3, 0, -5, -2, -3, 0, ...). A129691 * A126988 = A051731. Left column = A023900: (1, -1, -2, -1, -4, 2, -6, ...).

Examples

			First few rows of the triangle:
   1;
  -1,  1;
  -2,  0,  1;
  -1, -1,  0,  1;
  -4,  0,  0,  0,  1;
   2, -2, -1,  0,  0,  1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275

Crossrefs

Cf. A054523, A130055, A023900, A126988, A051731.

Programs

PARI

T(n,k)={if(n%k, 0, sumdivmult(n/k, d, d*moebius(d)))} \\ Andrew Howroyd, Aug 03 2018

Formula

A054523^(-1), as an infinite lower triangular matrix.

T(n,k) = A023900(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 03 2018

Extensions

Terms a(56) and beyond from Andrew Howroyd, Aug 03 2018