30

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Summary

The factorization is as follows, with factors 2, 3, and 5:

$30=2^{1}\cdot 3^{1}\cdot 5^{1}=2\cdot 3\cdot 5$

Property or family	Parameter values	First few members of the family	Proof of satisfaction/membership/containment
Giuga number: composite number $n$ such that $p$ divides $(n/p)-1$ for all prime divisors $p$ of $n$ .	first Giuga number	30, 858, 1722, 66198, [SHOW MORE] 2214408306, 24423128562, 432749205173838, 14737133470010574, 550843391309130318, 244197000982499715087866346, 554079914617070801288578559178, 1910667181420507984555759916338506 View list on OEIS	check on each prime divisor: 2 divides (30/2) - 1 = 14 3 divides (30/3) - 1 = 9 5 divides 30/5 - 1 = 5
primorial: product of the first few prime numbers	product of the first three prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the fourth in the list)	1, 2, 6, 30, 210, 2310 View list on OEIS	The first three primes are 2,3,5, and their product is 30.

Function	Value	Explanation
Euler totient function	8	The Euler totient function is $(2-1)(3-1)(5-1)=(1)(2)(4)=8$ .
universal exponent	4	The universal exponent is $\operatorname {lcm} \{(2-1),(3-1),(5-1)\}=4$ .
divisor count function	8	$(1+1)(1+1)(1+1)$ where the first 1s in both factors are the multiplicities of the prime divisors.
divisor sum function	72	$(2^{2}-1)/(2-1)$ times $(3^{2}-1)/(3-1)$ times $(5^{2}-1)/(5-1)$ equals $(3)(4)(6)=72$ .
Mobius function	-1	The number is square-free and has an odd number of prime divisors (3 prime divisors).