# Category:Euler Phi Function

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This category contains results about the Euler $\phi$ function.

Let $n \in \Z_{>0}$, that is, a strictly positive integer.

The **Euler $\phi$ (phi) function** is the arithmetic function $\phi: \Z_{>0} \to \Z_{>0}$ defined as:

- $\map \phi n = $ the number of strictly positive integers less than or equal to $n$ which are prime to $n$

That is:

- $\map \phi n = \card {S_n}: S_n = \set {k: 1 \le k \le n, k \perp n}$

## Subcategories

This category has the following 6 subcategories, out of 6 total.

### C

### E

### N

## Pages in category "Euler Phi Function"

The following 85 pages are in this category, out of 85 total.

### 4

### C

### E

- Euler Phi Function is Even for Argument greater than 2
- Euler Phi Function is Multiplicative
- Euler Phi Function of 104
- Euler Phi Function of 117
- Euler Phi Function of 135
- Euler Phi Function of 1364
- Euler Phi Function of 140
- Euler Phi Function of 148
- Euler Phi Function of 152
- Euler Phi Function of 164
- Euler Phi Function of 168
- Euler Phi Function of 2 times Odd Prime
- Euler Phi Function of 216
- Euler Phi Function of 228
- Euler Phi Function of 234
- Euler Phi Function of 248
- Euler Phi Function of 25,940
- Euler Phi Function of 252
- Euler Phi Function of 256
- Euler Phi Function of 264
- Euler Phi Function of 270
- Euler Phi Function of 315
- Euler Phi Function of 316
- Euler Phi Function of 33,817,088
- Euler Phi Function of 420
- Euler Phi Function of 5188
- Euler Phi Function of 52
- Euler Phi Function of 524
- Euler Phi Function of 525
- Euler Phi Function of 56
- Euler Phi Function of 616
- Euler Phi Function of 630
- Euler Phi Function of 666 equals Product of Digits
- Euler Phi Function of 72
- Euler Phi Function of 735
- Euler Phi Function of 824
- Euler Phi Function of 825
- Euler Phi Function of 84
- Euler Phi Function of 90
- Euler Phi Function of 944
- Euler Phi Function of 945
- Euler Phi Function of 975
- Euler Phi Function of Integer
- Euler Phi Function of Integer/Corollary
- Euler Phi Function of n equal to Euler Phi Function of n+3
- Euler Phi Function of Non-Square Semiprime
- Euler Phi Function of Prime
- Euler Phi Function of Prime Power
- Euler Phi Function of Prime Power/Corollary
- Euler Phi Function of Product with Prime
- Euler Phi Function of Product with Prime/Corollary
- Euler Phi Function of Square-Free Integer
- Euler Phi Function/Examples/Phi is 6
- Euler Phi Function/Table

### I

### N

### P

### S

- Schatunowsky's Theorem
- Sequences of 3 Consecutive Integers with Rising Phi
- Sequences of Three Consecutive Strictly Increasing Euler Phi Values
- Smallest Even Integer whose Euler Phi Value is not the Euler Phi Value of an Odd Integer
- Successive Solutions of Phi of n equals Phi of n + 2
- Sum of Euler Phi Function over Divisors
- Sum of Möbius Function over Divisors
- Sum of Möbius Function over Divisors/Lemma