8128 (number)
From Wikipedia, the free encyclopedia
| Cardinal | eight thousand one hundred [and] twenty-eight |
| Ordinal | 8128th (eight thousand one hundred [and] twenty-eighth) |
| Factorization |  |
| Divisors | 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 |
| Roman numeral |  |
| Binary | 1111111000000 |
| Octal | 17700 |
| Duodecimal | 4854 |
| Hexadecimal | 1FC0 |
8128 is the natural number following 8127 and preceding 8129.
It is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. 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.
Another consequence of 8128 being a perfect number is that it has the same prime factors as the sum of its divisors, its cototient is a power of two, and it is a harmonic seed number (though there are deficient and abundant numbers that share these properties).
8128 is the 127th triangular number, the 64th hexagonal number, the eighth 292-gonal number, and the fourth 1356-gonal number, as well as a centered nonagonal number.
