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Unital Sums of the Möbius and Mertens Functions
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Jeffery Kline

Madison, WI 53711

USA

**Abstract:**

We use standard techniques of linear algebra to construct an infinite
family of identities that involve finite weighted sums of the Möbius
and Mertens functions, where the weights are equal to −1, 0, or 1. In
a related manner, we construct, for each positive integer *n*,
an *n* × *n* symmetric unimodular matrix,
and each matrix is used to express an
identity that involves a finite weighted sum of the Möbius function. We
establish several results on the spectral decomposition of these matrices.

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(Concerned with sequences
A002321
A008683
A056594
A127473
A327580.)

Received September 21 2019; revised versions received September 22 2019; December 29
2019; July 7 2020.
Published in *Journal of Integer Sequences*,
August 7 2020.

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