Question: In the theory of numbers, square free numbers have a special place. A square free number is one that is not divisible by a perfect square (other than 1). Thus 72 is divisible by 36 (a perfect square), and is not a square free number, but 70 has factors 1, 2, 5, 7, 10, 14, 35 and 70. As none of these are perfect squares (other than 1), 70 is a square free number. For some algorithms, it is important to find out the square free numbers that divide a number. Note that 1 is not considered a square free number. In this problem, you are asked to write a program to find the number of square free numbers tha divide a given number.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Question: In the theory of numbers, square free numbers have a special place. A square free
number is one that is not divisible by a perfect square (other than 1). Thus 72 is divisible by 36 (a
perfect square), and is not a square free number, but 70 has factors 1, 2, 5, 7, 10, 14, 35 and 70. As
none of these are perfect squares (other than 1), 70 is a square free number.
For some algorithms, it is important to find out the square free numbers that divide a number.
Note that 1 is not considered a square free number.
In this problem, you are asked to write a program to find the number of square free numbers that
divide a given number.
Input
• The only line of the input is a single integer N which is divisible by no prime number
larger than 19
Output
• One line containing an integer that gives the number of square free numbers (not
including 1)
Constraints
●
Complexity
Simple
Time Limit
1
N 109
Example 1
Input
20
Output
3
Transcribed Image Text:Question: In the theory of numbers, square free numbers have a special place. A square free number is one that is not divisible by a perfect square (other than 1). Thus 72 is divisible by 36 (a perfect square), and is not a square free number, but 70 has factors 1, 2, 5, 7, 10, 14, 35 and 70. As none of these are perfect squares (other than 1), 70 is a square free number. For some algorithms, it is important to find out the square free numbers that divide a number. Note that 1 is not considered a square free number. In this problem, you are asked to write a program to find the number of square free numbers that divide a given number. Input • The only line of the input is a single integer N which is divisible by no prime number larger than 19 Output • One line containing an integer that gives the number of square free numbers (not including 1) Constraints ● Complexity Simple Time Limit 1 N 109 Example 1 Input 20 Output 3
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