8128 (number)

8128 (number)

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.

ee also

* 8128 Nicomachus


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