← 8127 8128 Factorization 2× 127 | 8128 8129 → | |
Cardinal eight thousand one hundred twenty-eight Ordinal 8128th
(eight thousand one hundred and twenty-eighth) Divisors 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 | ||
8128 is the integer 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, a happy number, the eighth 292-gonal number, and the fourth 1356-gonal number, as well as the 43rd centered nonagonal number.