##
**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 438.10036

**Autor: ** Erdös, Paul; Babu, Gutti Jogesh; Ramachandra, K.

**Title: ** An asymptotic formula in additive number theory. II. (In English)

**Source: ** J. Indian Math. Soc., New Ser. 41, 281-291 (1977).

**Review: ** [Part I, cf. Acta Arith. 28, 405-412 (1976; Zbl 278.10047)]

Let **{**b_{j}**}** be a sequence of integers satisfying 3 \leq b_{1} < b_{2} < b_{3} < ... and **sum**_{j = 1}^{oo}\frac 1{b_{j}} < oo. Suppose **sum**_{bj \leq x}1 = 0**(**\frac x{log x log log x}**)**. Then the authors prove that the equation n = p+t where p is a prime and t is an integer not divisible by any b_{j} has \frac{\alpha n}{log n}+o**(**\frac n{log n}**)** solutions and in particular has at least one solution for all sufficiently large n. Also the authors show that if a certain unproved hypothesis holds then the same result can be established under the slightly milder restriction **sum**_{bj \leq x}1 = o**(**\frac{x}{log x}**)**.

**Classif.: ** * 11P32 Additive questions involving primes

11N37 Asymptotic results on arithmetic functions

11N35 Sieves

**Keywords: ** Goldbach conjecture; Brun's Sieve; primitive abundant numbers

**Citations: ** Zbl.278.10047

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag