133 (one hundred
ndthirty-three) 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
132 and preceding
134.
In mathematics
133 is an ''n'' whose divisors (excluding ''n'' itself) added up divide
φ(''n''). It is an
octagonal number
In mathematics, an octagonal number is a figurate number. The ''n''th octagonal number ''o'n'' is the number of dots in a pattern of dots consisting of the outlines of regular octagons with sides up to ''n'' dots, when the octagons are overlai ...
and a
happy number
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...
.
133 is a
Harshad number
In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ...
, because it is divisible by the sum of its digits.
133 is a
repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit".
Ex ...
in
base 11 (111) and base 18 (77), whilst in
base 20 it is a
cyclic number formed from the
reciprocal of
the number three.
133 is a
semiprime: a product of two
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
s, namely 7 and 19. Since those prime factors are
Gaussian prime
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as \mathbf /ma ...
s, this means that 133 is a
Blum integer.
133 is the number of compositions of 13 into distinct parts.
References
{{DEFAULTSORT:133 (Number)
Integers