# Python Program to Print all Integers that Aren’t Divisible by Either 2 or 3

We can input a set of integer, and check which integers in this range, beginning with 1 are not divisible by 2 or 3, by checking the remainder of the integer with 2 and 3.

**Example:**

Input:10Output:Numbers not divisible by 2 and 3 1 5 7

**Method 1**: We check if the number is not divisible by 2 and 3 using the and clause, then outputs the number.

## Python3

`# input the maximum number to` `# which you want to send` `max_num ` `=` `20` `# starting numbers from 0` `n ` `=` `1` `# run until it reaches maximum number` `print` `(` `"Numbers not divisible by 2 and 3"` `)` `while` `n <` `=` `max_num:` ` ` ` ` `# check if number is divisible by 2 and 3` ` ` `if` `n ` `%` `2` `!` `=` `0` `and` `n ` `%` `3` `!` `=` `0` `:` ` ` `print` `(n)` ` ` ` ` `# incrementing the counter` ` ` `n ` `=` `n` `+` `1` |

**Output:**

Numbers not divisible by 2 and 3 1 5 7 11 13 17 19

**Time Complexity:** O(1)

**Auxiliary Space:** O(1)

**Method 2**: We traverse the odd numbers starting with 1 since even numbers are divisible by 2. So, we increment the for a loop by 2, traversing only odd numbers and check, which one of them is not divisible by 3. This approach is better than the previous one since it only iterates through half the number of elements in the specified range.

The following Python code illustrates this :

## Python3

`# input the maximum number to` `# which you want to send` `max_num ` `=` `40` `print` `(` `"Numbers not divisible by 2 or 3 : "` `)` `# run until it reaches maximum number` `# we increment the loop by +2 each time,` `# since odd numbers are not divisible by 2` `for` `i ` `in` `range` `(` `1` `, max_num, ` `2` `):` ` ` ` ` `# check if number is not divisible by 3` ` ` `if` `i ` `%` `3` `!` `=` `0` `:` ` ` `print` `(i)` |

**Output:**

Numbers not divisible by 2 or 3 : 1 5 7 11 13 17 19 23 25 29 31 35 37

**Time Complexity:** O(1)

**Auxiliary Space:** O(1)