On the distribution of the number of prime factors of sums

Authors:
P. Erdős, H. Maier and A. Sárközy

Journal:
Trans. Amer. Math. Soc. **302** (1987), 269-280

MSC:
Primary 11N60

DOI:
https://doi.org/10.1090/S0002-9947-1987-0887509-X

MathSciNet review:
887509

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Abstract: We continue a series of investigations by A. Balog and two of the authors (P. Erdös and A. Sárközy) on the arithmetic properties of the elements , where , , and "dense sequences."

The present paper transfers the famous Erdös-Kac theorem on the normal distribution of the number of distinct prime factors of integers to such "sum sequences."

**[1]**A. Balog and A. Sárközy,*On sums of sequences of integers*. III, Acta Math. Acad. Sci. Hungar.**44**(1984), 339-349. MR**764627 (86g:11056c)****[2]**P. D. T. A. Elliott,*Probabilistic number theory*. II, Springer-Verlag, 1980. MR**560507 (82h:10002b)****[3]**J. Erdös and M. Kac,*The Gaussian law of errors in the theory of additive number-theoretic functions*, Amer. J. Math.**62**(1940), 738-742. MR**0002374 (2:42c)****[4]**P. Erdös and A. Sárközy,*On divisibility properties of integers of the form*, Acta. Math. Acad. Sci. Hungar. (to appear).**[5]**K. Prachar,*Primzahlverteilung*, Springer-Verlag, 1957. MR**0087685 (19:393b)****[6]**R. A. Rankin,*The difference between consecutive prime numbers*, J. London Math. Soc.**13**(1938), 242-247.**[7]**A. Sárközy,*On the number of prime factors of integers of the form*, Studia Sci. Math. Hungar. (to appear).**[8]**A. Sárközy and C. L. Stewart,*On divisors of sums of integers*. II, J. Reine Angew. Math.**365**(1986), 171-191. MR**826157 (88f:11088)****[9]**I. M. Vinogradov,*The method of trigonometrical sums in the theory of numbers*, Interscience, New York, 1954.

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0887509-X

Article copyright:
© Copyright 1987
American Mathematical Society