6

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Summary

Factorization

The number 6 has the following factorization, with prime factors 2 and 3:

$6=2^{1}\cdot 3^{1}=2\cdot 3$

Properties and families

Property or family	Parameter values	First few members of the family	Proof of satisfaction/membership/containment
perfect number: number $n$ such that the divisor sum function of $n$ is $2n$	first perfect number		divisor sum is $1+2+3+6=12=2(6)$
primorial: product of the first few prime numbers	product of the first two prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the third in the list)	1, 2, 6, 30, 210, 2310 View list on OEIS	The first two primes are 2 and 3, and their product is 6.
factorial: product of the first few natural numbers	product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the fourth in the list)	1, 2, 6, 24, 120, 720, 5040, 40320, 362880, [SHOW MORE] 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000 View list on OEIS	$1\cdot 2\cdot 3=6$

Arithmetic functions

Function	Value	Explanation
Euler totient function	2	The Euler totient function is $(2-1)(3-1)=(1)(2)=2$.
universal exponent	2	The universal exponent is $\operatorname {lcm} \{(2-1),(3-1)\}=2$.
divisor count function	4	$(1+1)(1+1)$ where the first 1s in both factors are the multiplicities of the prime divisors.
divisor sum function	12	$(2^{2}-1)/(2-1)$ times $(3^{2}-1)/(3-1)$ equals $(3)(4)=12$.
Mobius function	1	The number is square-free and has an even number of prime divisors (2 prime divisors).