On the sum of divisors of the Mersenne numbers

Florian Luca

Mathematica Slovaca (2003)

  • Volume: 53, Issue: 5, page 457-466
  • ISSN: 0139-9918

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Luca, Florian. "On the sum of divisors of the Mersenne numbers." Mathematica Slovaca 53.5 (2003): 457-466. <http://eudml.org/doc/31788>.

@article{Luca2003,
author = {Luca, Florian},
journal = {Mathematica Slovaca},
keywords = {arithmetical function; Mersenne numbers; the sum of divisor function; Euler function; density},
language = {eng},
number = {5},
pages = {457-466},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On the sum of divisors of the Mersenne numbers},
url = {http://eudml.org/doc/31788},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Luca, Florian
TI - On the sum of divisors of the Mersenne numbers
JO - Mathematica Slovaca
PY - 2003
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 53
IS - 5
SP - 457
EP - 466
LA - eng
KW - arithmetical function; Mersenne numbers; the sum of divisor function; Euler function; density
UR - http://eudml.org/doc/31788
ER -

References

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  1. ERDÖS P., On the sum ∑ d | 2 n - 1 d - 1 , Israel J. Math. 9 (1971), 43-48. (1971) MR0269613
  2. ERDÖS P.-KISS P.-POMERANCE, C, On prime divisors of Mersenne numbers, Acta Arith. 57 (1991), 267-281. (1991) Zbl0733.11003MR1105611
  3. EVEREST G. R.-SHPARLINSKI I., Divisor sums of generalized exponential polynomials, Canad. Math. Bull. 39 (1996), 35-46. (1996) MR1382488
  4. von zur GATHEN J.-KNOPFMACHER A.-LUCA F.-LUCHT L.-SHPARLINSKI I., Average order in cyclic groups, J. Theor. Nombres Bordeaux (To appear). Zbl1079.11003
  5. LUCA F., Some mean values related to average multiplicative orders of elements in finite fields, Ramanujan J. (To appear). Zbl1155.11344MR2166376
  6. LUCA F.-SHPARLINSKI I., Arithmetical functions with linear recurrence sequences, Preprint, 2002. MR2332599
  7. MONTGOMERY H. L.-VAUGHAN R. C, The large sieve, Mathematika 20 (1973) 119-134. (1973) Zbl0296.10023MR0374060
  8. POMERANCE C., On primitive divisors of Mersenne numbers, Acta Arith. 46 (1986) 355-367. (1986) Zbl0606.10034MR0871278
  9. SHPARLINSKI I., The number of prime divisors of recurrence sequences, Mat. Zametki 38 (1985), 29-34. (Russian) (1985) MR0804177
  10. SHPARLINSKI I., The number of different prime divisors of recurrent sequences, Mat Zametki 42 (1987), 494-507. (Russian) (1987) MR0917803
  11. SHPARLINSKI I., Some arithmetic properties of recurrence sequences, Mat. Zametki 47 (1990), 124-131 (Russian). [Translation: Math. Notes 47 (1990), 612-617]. (1990) MR1074537
  12. TENENBAUM G., Introduction to Analytic and Probabilistic Number Theory, (Transl from the 2nd French ed. by C. B. Thomas). Cambridge Stud. Adv. Math. 46, Cambridge University Press, Cambridge, 1995. (1995) Zbl0880.11001MR1342300

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