6

6 (six) is a positive integer following 5 and preceding 7. Its ordinal form is written "sixth" or "6th".
== Properties ==
*6 is an , the third , the third factorial number, and 3 or 4 primorial.
*6 is equal to the sum of its proper divisors: 1 + 2 + 3 = 6. This makes it a MathWorld, Perfect Number, and in fact the smallest number with that property, with the next being 28.
*6 is equal to the sum of its unitary proper divisors, that is to say divisors d such that d and n/d are relatively prime. These are called unitary perfect numbers. It is the smallest number with this property.
*It is the only to not also be a .
*It is the smallest number N such that all multiples of N are . All perfect or abundant numbers have this property.
*In the Czech language, 6 is called "půltucet", meaning "half-twelve".
== In googology ==
*Some googologisms based on 6 are sextoogol, superhex and the hexalogue. It is not commonly found in googology.
*Six is the basis of Robert Munafo's idea of classes. 6 is the boundary between class 0 and class 1 numbers, 106 is the boundary between class 1 and class 2 numbers, 10106 is the boundary between class 2 and class 3 numbers, and so on.
*The Misalian seximal system uses base six, which is also called or heximal.
*In Greek-based number naming systems, 6 is associated with prefix hexa-, and with prefix sexti- in Latin systems.
*6 is the last digit of mega.
*Flan number 4 version 2 (or フラン数第四形態改二 in Japanese) is equal to 6. This started a joke in the Japanese googology community that 6 was a large number.叢武, 6は巨大数, twitter.
*６ (or 全角の6 in Japanese) is a specific value of a function in a version N3.0 of N primitive. The shape of the letter looks quite similar to 6, but the value is shown to be greater than 6.
=== Googological functions returning 6 ===
*Busy Beaver Function: \(\Sigma(3)=6\)
*Maximum shifts function: \(S(2)=6\)
*Subcubic graph number: \(\text{SCG}(0)=6\)
*Xi function: \(\Xi(5) = 6\)
== Sources ==
cs:6
es:6
zh:六
Category:Numbers
Category:Class 0
Category:Class 1
Category:Factorial numbers
Category:Numbers 0-99
Category:Numbers with 1 to 2 digits
Category:Perfect numbers
 
Category:Primorial numbers
Category:Superior highly composite numbers