# On Prefix-Free and Suffix-Free Sequences of Integers

• Rudolf Ahlswede
• Levon H. Khachatrian
• András Sárközy
Chapter

## Abstract

The set of the positive integers and positive square—free integers are denoted by IN and IN*, respectively, and we write IN(n) = IN ∩ [1, n], IN* (n) = IN* ∩ [1, n], where [1, n] = {1, 2, ... , n}. The set of primes is denoted by P. The smallest and greatest prime factors of the positive integer n are denoted by p(n) and P(n), respectively. ω(n) denotes the number of distinct prime factors of n, while Ω(n) denotes the number of prime factors of n counted with multiplicity:
$$\omega \left( n \right)\, = \,\sum\limits_{p|n} {1,} \,\Omega \left( n \right)\, = \,\sum\limits_{{p^\alpha }\parallel n} {\alpha .}$$
µ(n) denotes the Möbius function.

### Keywords

Prefix Univer Suffix Alsb

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