We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is very much like the one developed in Isabelle proof assistant connected with Avigad's formal proof of Prime Number Theorem) was done according to the book [13].
@article{bwmeta1.element.doi-10_2478_v10037-006-0005-0,
author = {Magdalena Jastrzebska and Adam Grabowski},
title = {On the Properties of the M\"obius Function},
journal = {Formalized Mathematics},
volume = {14},
year = {2006},
pages = {29-36},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0005-0}
}
Magdalena Jastrzebska; Adam Grabowski. On the Properties of the Möbius Function. Formalized Mathematics, Tome 14 (2006) pp. 29-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0005-0/
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