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# 219 (number)

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 Title: 219 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 219 (number)

 ← 218 219 220 →
Cardinal two hundred nineteen
Ordinal 219th
(two hundred and nineteenth)
Factorization 3 × 73
Roman numeral CCXIX
Binary 110110112
Ternary 220103
Quaternary 31234
Quinary 13345
Senary 10036
Octal 3338
Duodecimal 16312
Vigesimal AJ20
Base 36 6336

219 is the natural number following 218 and preceding 220.

## Mathematics

• Mertens function(219) = 4, a record high.[1]
• There are 219 partially ordered sets on four labeled elements.[2]
• 219 is the smallest number that can be represented as a sum of four positive cubes in two different ways.[3]
• There are 219 different space groups, discrete and full-dimensional sets of symmetries of three-dimensional space or of crystal structures.

## References

1. ^ "Sloane's A051400 : Smallest value of x such that M(x)=n, where M() is Mertens's function", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ "Sloane's A001035 : Number of partially ordered sets ("posets") with n labeled elements (or labeled acyclic transitive digraphs)", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ "Sloane's A025420 : Least sum of 4 positive cubes in exactly n ways", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
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