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Article

Banks, William D. ; Luca, Florian
On integers with a special divisibility property. (English). Archivum Mathematicum, vol. 42 (2006), issue 1, pp. 31-42
MSC: 11N37 | MR 2227110 | Zbl 1164.11050
Keywords:
Euler function; Carmichael function
Summary:
In this note, we study those positive integers $n$ which are divisible by $\sum _{d|n}\lambda (d)$, where $\lambda (\cdot )$ is the Carmichael function.
References:
[1] Bang A. S.: Taltheoretiske Undersøgelser. Tidsskrift Mat. 4 (5) (1886), 70–80, 130–137.
[2] De Koninck J. M., Luca F.: Positive integers divisible by the sum of their prime factors. Mathematika, to appear. MR 2261843
[3] Dickson L. E.: A new extension of Dirichlet’s theorem on prime numbers. Messenger of Math. 33 (1904), 155–161.
[4] Hardy G. H., Littlewood J. E.: Some problems on partitio numerorum III. On the expression of a number as a sum of primes. Acta Math. 44 (1923), 1–70. MR 1555183
[5] Ivić A.: The Riemann-Zeta Function, Theory and Applications. Dover Publications, Mineola, New York, 2003. MR 1994094 | Zbl 1034.11046
[6] Luca F., Pomerance C.: On the number of divisors of the Euler function. Publ. Math. Debrecen, to appear. MR 2288471
[7] Tenenbaum G.: Introduction to Analytic and Probabilistic Number Theory. Cambridge University Press, 1995. MR 1342300 | Zbl 0880.11001
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