On sums involving reciprocals of the largest prime factor of an integer II

Aleksandar Ivić

Acta Arithmetica (1995)

  • Volume: 71, Issue: 3, page 229-251
  • ISSN: 0065-1036

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Aleksandar Ivić. "On sums involving reciprocals of the largest prime factor of an integer II." Acta Arithmetica 71.3 (1995): 229-251. <http://eudml.org/doc/206771>.

@article{AleksandarIvić1995,
author = {Aleksandar Ivić},
journal = {Acta Arithmetica},
keywords = {sums involving reciprocals; largest prime factor of an integer; Riemann hypothesis; asymptotic formulas; Dickman function},
language = {eng},
number = {3},
pages = {229-251},
title = {On sums involving reciprocals of the largest prime factor of an integer II},
url = {http://eudml.org/doc/206771},
volume = {71},
year = {1995},
}

TY - JOUR
AU - Aleksandar Ivić
TI - On sums involving reciprocals of the largest prime factor of an integer II
JO - Acta Arithmetica
PY - 1995
VL - 71
IS - 3
SP - 229
EP - 251
LA - eng
KW - sums involving reciprocals; largest prime factor of an integer; Riemann hypothesis; asymptotic formulas; Dickman function
UR - http://eudml.org/doc/206771
ER -

References

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  1. [1] K. Alladi, The Turán-Kubilius inequality for integers without large prime factors, J. Reine Angew. Math. 335 (1982), 180-196. Zbl0483.10050
  2. [2] N. G. de Bruijn, On the number of positive integers ≤x and free of prime factors >y, Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951), 50-60. Zbl0042.04204
  3. [3] J.-M. De Koninck and A. Ivić, Topics in Arithmetical Functions, Math. Stud. 43, North-Holland, Amsterdam, 1980. 
  4. [4] J.-M. De Koninck and A. Ivić, The distribution of the average prime divisor of an integer, Arch. Math. (Basel) 43 (1984), 37-43. Zbl0519.10027
  5. [5] P. Erdős, A. Ivić and C. Pomerance, On sums involving reciprocals of the largest prime factor of an integer, Glas. Mat. 21 (41) (1986), 283-300. 
  6. [6] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307. Zbl0575.10038
  7. [7] A. Hildebrand and G. Tenenbaum, On a class of differential-difference equations arising in number theory, to appear. Zbl0797.11072
  8. [8] A. Ivić, Sum of reciprocals of the largest prime factor of an integer, Arch. Math. (Basel) 36 (1981), 57-61. 
  9. [9] A. Ivić, On some estimates involving the number of prime divisors of an integer, Acta Arith. 49 (1987), 21-33. 
  10. [10] A. Ivić and C. Pomerance, Estimates for certain sums involving the largest prime factor of an integer, in: Topics in Classical Number Theory, Colloq. Math. Soc. János Bolyai 34, North-Holland, Amsterdam, 1984, 769-789. 
  11. [11] E. Saias, Sur le nombre des entiers sans grand facteur premier, J. Number Theory 32 (1989), 78-99. Zbl0676.10028
  12. [12] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Inst. Élie Cartan 13, Université de Nancy, 1990. 
  13. [13] T. Z. Xuan, Estimates of certain sums involving reciprocals of the largest prime factor of an integer, J. Beijing Normal Univ. (N.S.) 1 (1988), 11-16 (in Chinese). Zbl0684.10045
  14. [14] T. Z. Xuan, On sums involving reciprocals of certain large additive functions, Publ. Inst. Math. (Belgrade) 45 (59) (1989), 41-55 and II, Publ. Inst. Math. (Belgrade) 46 (60) (1989), 25-32. 

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