128 (one hundred [and] twenty-eight) is the natural number following 127 and preceding 129.

← 127 128 129 →
Cardinalone hundred twenty-eight
(one hundred twenty-eighth)
Divisors1, 2, 4, 8, 16, 32, 64, 128
Greek numeralΡΚΗ´
Roman numeralCXXVIII

In mathematics Edit

128 is the seventh power of 2. It is the largest number which cannot be expressed as the sum of any number of distinct squares.[1][2] However, it is divisible by the total number of its divisors, making it a refactorable number.[3]

The sum of Euler's totient function φ(x) over the first twenty integers is 128.[4]

128 can be expressed by a combination of its digits with mathematical operators, thus 128 = 28 − 1, making it a Friedman number in base 10.[5]

A hepteract has 128 vertices.

128 is the only 3-digit number that is a 7th power (27).

In bar codes Edit

  • Code 128 is a Uniform Symbology Specification (USS Code 128) alphanumeric bar code that encodes text, numbers, numerous functions, and designed to encode all 128 ASCII characters (ASCII 0 to ASCII 127), as used in the shipping industry.
  • Subdivisions include:

In computing Edit

All 128 possible states of the seven-segment display.

In the military Edit

In transportation Edit

In other fields Edit

One hundred [and] twenty-eight is also:

See also Edit

Notes Edit

  1. ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z., 51 (3): 289–290, doi:10.1007/BF01181594, MR 0027285, S2CID 123515191
  2. ^ OEIS:A001422. Similarly, the largest numbers that cannot be expressed as sums of distinct cubes and fourth powers, respectively, are 12758 and 5134240 (sequence A001661 in the OEIS).
  3. ^ OEIS:A033950.
  4. ^ OEIS:A002088.
  5. ^ OEIS:A036057.

References Edit

External links Edit