Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.1

Unital Sums of the Möbius and Mertens Functions

Jeffery Kline
Madison, WI 53711


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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