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# 128 (number)

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 Title: 128 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 128 (number)

 ← 127 128 129 →
Cardinal one hundred twenty-eight
Ordinal 128th
(one hundred and twenty-eighth)
Factorization 27
Divisors 1, 2, 4, 8, 16, 32, 64, 128
Roman numeral CXXVIII
Binary 100000002
Ternary 112023
Quaternary 20004
Quinary 10035
Senary 3326
Octal 2008
Duodecimal A812
Hexadecimal 8016
Vigesimal 6820
Base 36 3K36

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

## Contents

• In mathematics 1
• In bar codes 2
• In computing 3
• In the military 4
• In transportation 5
• In other fields 6
• See also 7
• Notes 8
• References 9
• External links 10

## 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.

## In other fields

One hundred [and] twenty-eight is also:

## Notes

1. ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z. 51 (3): 289–290,
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 OEIS).
3. ^ OEIS:A033950.
4. ^ OEIS:A002088.
5. ^ OEIS:A036057.

## References

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