Journal of Integer Sequences, Vol. 16 (2013), Article 13.6.3

An Alternating Sum Involving the Reciprocal of Certain Multiplicative Functions


Olivier Bordellès
2, allée de la Combe
43000 Aiguilhe
France

Benoit Cloitre
19, rue Louise Michel
92300 Levallois-Perret
France

Abstract:

We establish an asymptotic formula for an alternating sum of the reciprocal of a class of multiplicative functions. The proof is straightforward and uses classical convolution techniques. Numerous examples are given.

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(Concerned with sequences A001615 A058026 A065463 A082695 A211117 A211178.)

Received February 9 2013; revised version received March 3 2013; June 12 2013. Published in Journal of Integer Sequences, June 16 2013.

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