## Some Properties of the Möbius Function

In this section, we will provide some further elementary properties of the Möbius function and derive the useful Möbius inversion formula for arithmetic functions.

| | | | created: 2019-04-06 08:41:03 | modified: 2019-04-06 22:37:14 | by: *bookofproofs* | references: [701], [1272]

## 1.**Proposition**: Sum of Möbius Function Over Divisors

## 2.**Lemma**: Sum of Möbius Function Over Divisors With Division

## 3.**Lemma**: Möbius and Floor Functions Combined

## 4.**Lemma**: Upper Bound of Harmonic Series Times Möbius Function

## 5.**Theorem**: Möbius Inversion Formula

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[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

[701] **Scheid Harald**: “Zahlentheorie”, Spektrum Akademischer Verlag, 2003, 3. Auflage

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