30
This article is about a particular natural number.|View all articles on particular natural numbers
Summary
Factorization
The factorization is as follows, with factors 2, 3, and 5:
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 30 = 2^1 \cdot 3^1 \cdot 5^1 = 2 \cdot 3 \cdot 5}
Properties and families
| Property or family | Parameter values | First few members of the family | Proof of satisfaction/membership/containment |
|---|---|---|---|
| Giuga number: composite number Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} such that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} divides Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (n/p) - 1} for all prime divisors Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} . | first Giuga number | 30, 858, 1722, 66198, [SHOW MORE]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. |
Arithmetic functions
| Function | Value | Explanation |
|---|---|---|
| Euler totient function | 8 | The Euler totient function is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2 - 1)(3 - 1)(5 - 1) = (1)(2)(4) = 8} . |
| universal exponent | 4 | The universal exponent is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \operatorname{lcm}\{(2 - 1),(3 - 1),(5-1) \} = 4} . |
| divisor count function | 8 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1 + 1)(1 + 1)(1 + 1)} where the first 1s in both factors are the multiplicities of the prime divisors. |
| divisor sum function | 72 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2^2-1)/(2-1)} times Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (3^2 - 1)/(3 - 1)} times Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (5^2 - 1)/(5 - 1)} equals Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (3)(4)(6) = 72} . |
| Mobius function | -1 | The number is square-free and has an odd number of prime divisors (3 prime divisors). |