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128 (number)

← 127 128 129 →
Cardinalone hundred twenty-eight
Ordinal128th
(one hundred twenty-eighth)
Factorization27
Divisors1, 2, 4, 8, 16, 32, 64, 128
Greek numeralΡΚΗ´
Roman numeralCXXVIII
Binary100000002
Ternary112023
Quaternary20004
Quinary10035
Senary3326
Octal2008
DuodecimalA812
Hexadecimal8016
Vigesimal6820
Base 363K36

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

In mathematics

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] But 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

  • 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

In the military

In transportation

In other fields

One hundred [and] twenty-eight is also:

See also

Notes

  1. ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z., 51 (3): 289–290, doi:10.1007/BF01181594, MR 0027285
  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

External links