A144735 - OEIS

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

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OFFSET

1,2

COMMENTS

Row sums = A008683, mu(n).

Right border = squares of phi(n).

LINKS

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

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

EXAMPLE

First few rows of the triangle are as follows:

-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;

...