8128
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| Cardinal | eight thousand one hundred twenty-eight | |||
| Ordinal | 8128th (eight thousand one hundred twenty-eighth) | |||
| Factorization | 26 × 127 | |||
| Divisors | 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 | |||
| Greek numeral | ,ΗΡΚΗ´ | |||
| Roman numeral | VMMMCXXVIII, or VIIICXXVIII | |||
| Binary | 11111110000002 | |||
| Ternary | 1020110013 | |||
| Senary | 1013446 | |||
| Octal | 177008 | |||
| Duodecimal | 485412 | |||
| Hexadecimal | 1FC016 | |||
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.[1]
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.[2]
See also
References
- ^ "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.