219 (number) explained

219 (two hundred [and] nineteen) is the natural number following 218 and preceding 220.

In mathematics

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

Notes and References

1. Happy numbers.
2. A051400. Smallest value of x such that M(x)=n, where M is Mertens's function.
3. A001035. Number of partially ordered sets ("posets") with n labeled elements (or labeled acyclic transitive digraphs).
4. A025420. Least sum of 4 positive cubes in exactly n ways. .