# Mertens function

From Number

This article is about a function defined on positive reals (and in particular, natural numbers) obtained as the summatory function of an arithmetic function, namely Mobius function.

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## Definition

Let be a positive real number. The **Mertens function** of , denoted , is defined as:

.

Here, denotes the Mobius function.

We typically evaluate the Mertens function for natural numbers.

## Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A002321