8128

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← 812781288129 →
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 (its divisors 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, and 4064 add up to 8128), 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

Related Research Articles

28 (twenty-eight) is the natural number following 27 and preceding 29.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

127 is the natural number following 126 and preceding 128. It is also a prime number.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number.

2000 is a natural number following 1999 and preceding 2001.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.

5000 is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic numeral in the English language.

6000 is the natural number following 5999 and preceding 6001.

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204 is the natural number following 203 and preceding 205.

30,000 is the natural number that comes after 29,999 and before 30,001.

50,000 is the natural number that comes after 49,999 and before 50,001.

References

  1. ↑ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-03.
  2. ↑ "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.
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