A144735 Square of triangle A054533 (matrix square), read by rows.

1, -2, 1, -2, -3, 4, 2, -6, 0, 4, -3, -2, -6, -6, 16, 5, 0, -9, -5, 6, 4, -5, -2, -5, -6, -11, -8, 36, 0, 8, 0, -24, 0, 0, 0, 16, 0, 6, -18, 3, -3, -24, 0, 0, 36, 7, 0, 8, 2, -34, -10, 10, -8, 10, 16

Offset: 1

Author

Gary W. Adamson, Sep 20 2008

Keywords

• tabl
• sign
• more

Comments

Row sums = A008683, mu(n).

Right border = squares of phi(n).

Examples

			First few rows of the triangle are as follows:
   1;
  -2,  1;
  -2, -3,   4;
   2, -6,   0,   4;
  -3, -2,  -6,  -6,  16;
   5,  0,  -9,  -5,   6,   4;
  -5, -2,  -5,  -6, -11,  -8, 36;
   0,  8,   0, -24,   0,   0,  0, 16;
   0,  6, -18,   3,  -3, -24,  0,  0, 36;
   7,  0,   8,   2, -34, -10, 10, -8, 10, 16;
   ...
		

Crossrefs

Cf. A008683, A054533.

Formula

A054533^2, as an infinite lower triangular matrix.

T(n, k) = Sum_{s = k..n} R(n, s) * R(s, k) for n >= 1 and 1 <= k <= n, where R(n, s) = A054533(n, s) = Sum_{d | gcd(n,s)} d * mu(n/d). - Petros Hadjicostas, Jul 29 2019