A144733 Triangle read by rows, 2*A054533 - A054521.

1, -3, 2, -3, -3, 4, -1, -4, -1, 4, -3, -3, -3, -3, 8, 1, -2, -4, -2, 1, 4, -3, -3, -3, -3, -3, -3, 12, -1, 0, -1, -8, -1, 0, -1, 8, -1, -1, -6, -1, -1, -6, -1, -1, 12, 1, -2, 1, -2, -8, -2, 1, -2, 1, 8, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 20

Offset

1,2

Comments

Right border = A140434: (1, 2, 4, 4, 8, 4, 12,...).

Left border = A133695: (1, -3, -3, -1, -3, 1, -3, -1,...)

Row sums = A000010, with negative signs after the first 1: (1, -1, -2, -2, -4, -2, -6,...).

Links

Table of n, a(n) for n=1..66.

Formula

Triangle read by rows, 2*A054533 - A054521; as infinite lower triangular matrices.

T(n,k) = -I(gcd(n,k) = 1) + 2 * Sum_{d|gcd(n,k)} d * mu(n/d) for n >= 1 and 1 <= k <= n, where I(condition) = 1 if the condition holds, and 0 otherwise. - Petros Hadjicostas, Jul 29 2019

Example

First few rows of the triangle =
   1;
  -3,  2;
  -3, -3,  4;
  -1, -4, -1,  4;
  -3, -3, -3, -3,  8;
   1, -2, -4, -2,  1,  4;
  -3, -3, -3, -3, -3, -3, 12;
  -1,  0, -1, -8  -1,  0, -1,  8;
  -1, -1, -6, -1, -1, -6, -1, -1, 12;
   1, -2,  1, -2, -8, -2,  1, -2,  1,  8;
  -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 20;
   ...

Crossrefs

Cf. A000010, A054521, A054532, A054533, A054534, A054535, A140434, A133695.

Sequence in context: A370231 A117451 A130970 * A091460 A035093 A292511

Adjacent sequences: A144730 A144731 A144732 * A144734 A144735 A144736

Keyword

tabl,sign

Author

Gary W. Adamson, Sep 20 2008

Status

approved