8128
From HandWiki
8128 (eight thousand one hundred [and] twenty-eight) is the natural number and integer following 8127 and preceding 8129.
In mathematics
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. 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
References
- ↑ Sloane, N. J. A., ed. "Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)". OEIS Foundation. https://oeis.org/A000396.
- ↑ Koninck, J. M. de (2009). Those fascinating numbers. Internet Archive. Providence, R.I. : American Mathematical Society. p. 177. ISBN 978-0-8218-4807-4. https://archive.org/details/thosefascinating0000koni/page/176/mode/2up.
- ↑ "What's Special About This Number?". https://erich-friedman.github.io/numbers.html.
- ↑ Vanovschi, Vitalii. "Properties of the number 8128" (in en). http://www.numberempire.com:80/8128.
- ↑ Bandyopadhyay, Santanu (2021-11-28). Perfect Numbers. Powai, Mumbai, 400076, India: Department of Energy Science and Engineering, Indian Institute of Technology Bombay. p. 1. https://www.ese.iitb.ac.in/~santanu/RM10.pdf. Retrieved 2026-08-20.
- ↑ "Sloane's A001599 : Harmonic or Ore numbers". OEIS Foundation. https://oeis.org/A001599.
 |  |
