8128
| ||||
|---|---|---|---|---|
| Cardinal | eight thousand one hundred twenty-eight | |||
| Ordinal | 8128th (eight thousand one hundred twenty-eighth) | |||
| Factorization | 26 × 127 | |||
| Divisors | 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064, 8128 | |||
| Greek numeral | ,ΗΡΚΗ´ | |||
| Roman numeral | VMMMCXXVIII, or VIIICXXVIII | |||
| Binary | 11111110000002 | |||
| Ternary | 1020110013 | |||
| Senary | 1013446 | |||
| Octal | 177008 | |||
| Duodecimal | 485412 | |||
| Hexadecimal | 1FC016 | |||
8128 (eight thousand one hundred [and] twenty-eight) is the natural number and integer following 8127 and preceding 8129.
In mathematics
[edit]It is most notable for being the fourth perfect number[1][2][3] (its proper divisors 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, and 4064 add up to 8128),[4] and one of the earliest numbers to be recognized as such.[5] As a perfect number, it is tied to the Mersenne prime 127, 27 – 1, with 26 (27 – 1) yielding 8128.[citation needed] Also related to its being a perfect number, 8128 is a harmonic divisor number.[6]
Another consequence of 8128 being a perfect number is that it has the same prime factors as the sum of its divisors, and its cototient is a power of two.
See also
[edit]References
[edit]- ↑ Sloane, N. J. A. (ed.). "Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Koninck, J. M. de (2009). Those fascinating numbers. Internet Archive. Providence, R.I. : American Mathematical Society. p. 177. ISBN 978-0-8218-4807-4.
- ↑ "What's Special About This Number?". erich-friedman.github.io. Retrieved 2026-07-19.
- ↑ Vanovschi, Vitalii. "Properties of the number 8128". www.numberempire.com. Retrieved 2026-08-22.
- ↑ Bandyopadhyay, Santanu (2021-11-28). Perfect Numbers (PDF). Powai, Mumbai, 400076, India: Department of Energy Science and Engineering, Indian Institute of Technology Bombay. p. 1. Retrieved 2026-08-20.
{{cite book}}: CS1 maint: location (link) - ↑ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-03.
| |||||||||
| |||||||||
| |||||||||
| |||||||||
 | This article about a number is a stub. You can help Wikipedia by adding missing information. |