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The distribution of the average prime divisor of an integer. (English) Zbl 0519.10027


MSC:

11N05 Distribution of primes
11N37 Asymptotic results on arithmetic functions

Citations:

Zbl 0442.10032
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Full Text: DOI

References:

[1] K. Alladi andP. Erdös, On an additive arithmetic function. Pacific J. Math.71, 275–294 (1977). · Zbl 0359.10038
[2] N. G. de Bruijn, On the number of positive integers and free of prime factors >y. Indag. Math.13, 50–60 (1951) and II ibid.28, 239–247 (1966). · Zbl 0042.04204
[3] J.-M. De Koninck, P. Erdös andA. Ivić, Reciprocals of large additive functions. Canadian Math. Bull.24, 225–231 (1981). · Zbl 0463.10032 · doi:10.4153/CMB-1981-035-7
[4] J.-M.De Koninck and A.Ivić, Topics in arithmetical functions. Notás de Matemática72, Amsterdam 1980.
[5] J.-M.De Koninck et A.Ivić, Sommes de réciproques de grandes fonctions additives. Publs. Inst. Mathém. Belgrade 35 (1984), in print.
[6] P. Erdös andA. Ivić, Estimates for sums involving the largest prime factor of an integer and certain related additive functions. Studia Scien. Math. Hungarica15, 183–199 (1980).
[7] P. Erdös andA. Ivić, On sums involving reciprocals of certain arithmetical functions. Publs. Inst. Mathém. Belgrade32, 49–56 (1982). · Zbl 0506.10035
[8] P.Erdös, A.Ivić and C.Pomerance, On sums involving reciprocals of the largest prime factor of an integer. To appear.
[9] A. Ivić, Sums of reciprocals of the largest prime factor of an integer. Arch. Math.36, 57–61 (1980).
[10] A.Ivić and C.Pomerance, Estimates of certain sums involving the largest prime factor of an integer. Coll. Math. Soc. J. Bolyai34, Topics in classical number theory, Amsterdam 1984. · Zbl 0546.10037
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