206 (two hundred
ndsix) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
205 and preceding
207
Year 207 (Roman numerals, CCVII) was a common year starting on Thursday of the Julian calendar. At the time, it was known in Rome as the Year of the Consulship of Maximus and Severus (or, less frequently, year 960 ''Ab urbe condita''). The deno ...
.
In mathematics
206 is both a
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie ...
and a
noncototient
In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function
In number theory ...
. 206 is an
untouchable number
In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their study goes back at l ...
. It is the lowest positive integer (when written in English as "two hundred and six") to employ all of the vowels once only, not including
Y. The other numbers sharing this property are 230, 250, 260, 602, 640, 5000, 8000, 9000, 26,000, 80,000 and 90,000. 206 and 207 form the second pair of consecutive numbers (after 14 and 15) whose
sums of divisors are equal. There are exactly 206 different
linear forests on five labeled nodes, and exactly 206
regular semigroup In mathematics, a regular semigroup is a semigroup ''S'' in which every element is regular, i.e., for each element ''a'' in ''S'' there exists an element ''x'' in ''S'' such that . Regular semigroups are one of the most-studied classes of semigroup ...
s of order four up to isomorphism and anti-isomorphism.
References
Integers
{{Num-stub