# 128 (number)

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128 (number)

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

128
Cardinal one hundred [and] twenty-eight
Ordinal 128th
(one hundred [and] twenty-eighth)
Numeral system 128
Factorization 27
Divisors 1, 2, 4, 8, 16, 32, 64, 128
Roman numeral CXXVIII
Binary 100000002
Octal 2008
Duodecimal A812

## In mathematics

One hundred [and] twenty-eight 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. 2 to the 7th power.

## 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 128.), as used in the shipping industry.
• International Symbology Specification Code (ISS Code) 128 is the USS Code for encoding of extended non-English ASCII characters

## In other fields

One hundred [and] twenty-eight is also:

## Notes

1. ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z. 51: 289–290, doi:10.1007/BF01181594, MR0027285
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

Wikimedia Foundation. 2010.

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