The Open Mathematics Journal

2008, 1 : 25-34
Published online 2008 September 16. DOI: 10.2174/1874117400801010025
Publisher ID: TOMATJ-1-25

Recursive formulas related to the summation of the mobius function

Manuel benito and Juan l. Varona

ABSTRACT

For positive integers n, let μ(n) be the Mobius function, and M(n) its sum M(n) = ∑n k=1 μ(k). We find some identities and recursive formulas for computing M(n); in particular, we present a two-parametric family of recursive formulas.

Keywords:

Möobius function, summation of the Möobius function, Mertens function.