219 (number)

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← 218 219 220 →
Cardinaltwo hundred nineteen
Ordinal219th
(two hundred nineteenth)
Factorization3 × 73
Greek numeralΣΙΘ´
Roman numeralCCXIX
Binary110110112
Ternary220103
Quaternary31234
Quinary13345
Senary10036
Octal3338
Duodecimal16312
HexadecimalDB16
VigesimalAJ20
Base 366336

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

Mathematics[edit]

  • 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.

See also[edit]

References[edit]

  1. ^ Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence 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.
  3. ^ Sloane, N. J. A. (ed.). "Sequence 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.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A025420 (Least sum of 4 positive cubes in exactly n ways)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..