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**1 - 2**of**2**### Sieve Methods

"... Sieve methods have had a long and fruitful history. The sieve of Eratosthenes (around 3rd century B.C.) was a device to generate prime numbers. Later Legendre used it in his studies of the prime number counting function π(x). Sieve methods bloomed and became a topic of intense investigation after th ..."

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Sieve methods have had a long and fruitful history. The sieve of Eratosthenes (around 3rd century B.C.) was a device to generate prime numbers. Later Legendre used it in his studies of the prime number counting function π(x). Sieve methods bloomed and became a topic of intense investigation after the pioneering work of Viggo Brun (see [Bru16],[Bru19], [Bru22]). Using his formulation of the sieve Brun proved, that the sum

### COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 51. NUMBER THEORY, BUDAPEST (HUNGARY), I987 THE DISTRIBUTION OF VALUES OF A CERTAIN CLASS OF ARITHMETIC FUNCTIONS AT CONSECUTIVE INTEGERS

"... The purpose of this paper is to study several aspects of the problem of the distribution of values of certain arithmetic functions, especially of the values at consecutive integers. Our main motivation is the ..."

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The purpose of this paper is to study several aspects of the problem of the distribution of values of certain arithmetic functions, especially of the values at consecutive integers. Our main motivation is the