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

Yvonne Buttkewitz; Christian Elsholtz; Kevin Ford; Jan Christoph Schlage-Puchta

doi:10.1093/imrn/rnr175

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

Yvonne Buttkewitz
, Christian Elsholtz
, Kevin Ford
, Jan Christoph Schlage-Puchta

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We determine asymptotically the maximal order of, where d(n) is the number of positive divisors of n. This solves a problem first put forth by Ramanujan in 1915.

Original language	English (US)
Pages (from-to)	4051-4061
Number of pages	11
Journal	International Mathematics Research Notices
Volume	2012
Issue number	17
DOIs	https://doi.org/10.1093/imrn/rnr175
State	Published - Sep 2012

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General Mathematics

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10.1093/imrn/rnr175

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title = "A problem of Ramanujan, Erds, and K{\'a}tai on the iterated divisor function",

abstract = "We determine asymptotically the maximal order of, where d(n) is the number of positive divisors of n. This solves a problem first put forth by Ramanujan in 1915.",

author = "Yvonne Buttkewitz and Christian Elsholtz and Kevin Ford and Schlage-Puchta, \{Jan Christoph\}",

note = "The work of Y. B. and C. E. was supported by the German Research Council (DFG-Grant-Number BU2488/1-3). K. F. was supported by National Science Foundation grant DMS-0901339.",

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N1 - The work of Y. B. and C. E. was supported by the German Research Council (DFG-Grant-Number BU2488/1-3). K. F. was supported by National Science Foundation grant DMS-0901339.

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

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