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|Cardinal||eight thousand one hundred twenty-eight|
(eight thousand one hundred twenty-eighth)
|Divisors||1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064|
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).
- "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-03.
- "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-03.