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	$2^6 \cdot 127$
Divisors	2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064
Roman numeral	$\overline{\mbox{VIII}}\mbox{CXXVIII}$
Binary
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.