| Title:
|
On the sum of divisors of the Mersenne numbers (English) |
| Author:
|
Luca, Florian |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
53 |
| Issue:
|
5 |
| Year:
|
2003 |
| Pages:
|
457-466 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11A25 |
| idZBL:
|
Zbl 1061.11005 |
| idMR:
|
MR2038513 |
| . |
| Date available:
|
2009-09-25T14:16:43Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/129330 |
| . |
| Reference:
|
[1] ERDÖS P.: On the sum $\sum_{d|2^n-1} d^{-1}$.Israel J. Math. 9 (1971), 43-48. MR 0269613 |
| Reference:
|
[2] ERDÖS P.-KISS P.-POMERANCE, C: On prime divisors of Mersenne numbers.Acta Arith. 57 (1991), 267-281. Zbl 0733.11003, MR 1105611 |
| Reference:
|
[3] EVEREST G. R.-SHPARLINSKI I.: Divisor sums of generalized exponential polynomials.Canad. Math. Bull. 39 (1996), 35-46. MR 1382488 |
| Reference:
|
[4] von zur GATHEN J.-KNOPFMACHER A.-LUCA F.-LUCHT L.-SHPARLINSKI I.: Average order in cyclic groups.J. Theor. Nombres Bordeaux (To appear). Zbl 1079.11003 |
| Reference:
|
[5] LUCA F.: Some mean values related to average multiplicative orders of elements in finite fields.Ramanujan J. (To appear). Zbl 1155.11344, MR 2166376 |
| Reference:
|
[6] LUCA F.-SHPARLINSKI I.: Arithmetical functions with linear recurrence sequences.Preprint, 2002. MR 2332599 |
| Reference:
|
[7] MONTGOMERY H. L.-VAUGHAN R. C : The large sieve.Mathematika 20 (1973) 119-134. Zbl 0296.10023, MR 0374060 |
| Reference:
|
[8] POMERANCE C.: On primitive divisors of Mersenne numbers.Acta Arith. 46 (1986) 355-367. Zbl 0606.10034, MR 0871278 |
| Reference:
|
[9] SHPARLINSKI I.: The number of prime divisors of recurrence sequences.Mat. Zametki 38 (1985), 29-34. (Russian) MR 0804177 |
| Reference:
|
[10] SHPARLINSKI I.: The number of different prime divisors of recurrent sequences.Mat Zametki 42 (1987), 494-507. (Russian) MR 0917803 |
| Reference:
|
[11] SHPARLINSKI I.: Some arithmetic properties of recurrence sequences.Mat. Zametki 47 (1990), 124-131 (Russian). [Translation: Math. Notes 47 (1990), 612-617]. MR 1074537 |
| Reference:
|
[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. Zbl 0880.11001, MR 1342300 |
| . |
