A130094 A051731 * an infinite lower triangular matrix with A007427 in the main diagonal.

1, 1, -2, 1, 0, -2, 1, -2, 0, 1, 1, 0, 0, 0, -2, 1, -2, -2, 0, 0, 4, 1, 0, 0, 0, 0, 0, -2, 1, -2, 0, 1, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, -2, 0, 0, 0, 0, 4

Offset

1,3

Comments

Right border = A007427. Row sums = mu(n), A008683. Nonzero terms by rows are substituted for the factors of n such that row sums = mu(n). Example: for row 6 we map (1, -2, -2, 0, 4), sum = 1, since the factors of 6 are 1, 2, 3 and 6.

Links

Table of n, a(n) for n=1..55.

Formula

Inverse Möbius transform of a triangular matrix with A007427 in the main diagonal and the rest zeros.

Example

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

Crossrefs

Cf. A007427, A008683, A051731.

Sequence in context: A185204 A217522 A287520 * A337005 A366745 A230025

Adjacent sequences: A130091 A130092 A130093 * A130095 A130096 A130097

Keyword

tabl,sign

Author

Gary W. Adamson, May 06 2007

Status

approved