- Title
- Principal divisor ranks of the first trillion positive integers
- Creator
- Eggleton, Roger B.; Kimberley, Jason S.; MacDougall, James A.
- Resource Type
- report
- Date
- 2009
- Description
- The principal divisors of a positive integer n are its maximal prime-power divisors. The principal divisor rank ω(n) is the number of such divisors, also equal to the number of distinct prime divisors of n. Building upon recent results on maximal runs of consecutive integers with equal rank, the present report describes eight types of pattern (including plateaux, peaks, valleys, and voids) which may occur in the sequence of ranks of consecutive integers, and determines the earliest instances of these patterns occurring within the positive integers up to 10^12. In particular, among the plateaux, starting at 585 927 201 062 there is a run of 23 consecutive integers of rank 4; there is no other constant rank run of size greater than 19 below 10^12.
- Subject
- Number Theory; distinct prime divisors; AMS 2000 MSC: 11A51
- Identifier
- http://hdl.handle.net/1959.13/35886
- Identifier
- uon:4185
- Rights
- Licensed under an Australian Creative Commons: Attribution Licence. http://creativecommons.org/licenses/by/2.5/au/
- Language
- eng
- Full Text
- Hits: 2887
- Visitors: 3142
- Downloads: 335
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Author final version | 369 KB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Author final version | 2 MB | Adobe Acrobat PDF | View Details Download |