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A problem of Ramanujan, Erdõs and Kátai on the iterated divisor function

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Abstract
We determine asymptotically the maximal order of log d(d(n)), where d(n) is the number of positive divisors of n. This solves a problem first put forth by Ramanujan in 1915.
Keywords
iterated divisor function, arithmetic functions, maximal order, Number of divisors

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Chicago
Buttkewitz, Yvonne, Christian Elsholtz, Kevin Ford, and Jan-Christoph Schlage-Puchta. 2012. “A Problem of Ramanujan, Erdõs and Kátai on the Iterated Divisor Function.” International Mathematics Research Notices (17): 4051–4061.
APA
Buttkewitz, Y., Elsholtz, C., Ford, K., & Schlage-Puchta, J.-C. (2012). A problem of Ramanujan, Erdõs and Kátai on the iterated divisor function. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, (17), 4051–4061.
Vancouver
1.
Buttkewitz Y, Elsholtz C, Ford K, Schlage-Puchta J-C. A problem of Ramanujan, Erdõs and Kátai on the iterated divisor function. INTERNATIONAL MATHEMATICS RESEARCH NOTICES. 2012;(17):4051–61.
MLA
Buttkewitz, Yvonne, Christian Elsholtz, Kevin Ford, et al. “A Problem of Ramanujan, Erdõs and Kátai on the Iterated Divisor Function.” INTERNATIONAL MATHEMATICS RESEARCH NOTICES 17 (2012): 4051–4061. Print.
@article{1989726,
  abstract     = {We determine asymptotically the maximal order of log d(d(n)), where d(n) is the number of positive divisors of n. This solves a problem first put forth by Ramanujan in 1915.},
  author       = {Buttkewitz, Yvonne and Elsholtz, Christian and Ford, Kevin and Schlage-Puchta, Jan-Christoph},
  issn         = {1073-7928},
  journal      = {INTERNATIONAL MATHEMATICS RESEARCH NOTICES},
  keyword      = {iterated divisor function,arithmetic functions,maximal order,Number of divisors},
  language     = {eng},
  number       = {17},
  pages        = {4051--4061},
  title        = {A problem of Ramanujan, Erd{\~o}s and K{\'a}tai on the iterated divisor function},
  url          = {http://dx.doi.org/10.1093/imrn/rnr175},
  year         = {2012},
}

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