Practice
Resources
Contests
Online IDE
New
Free Mock
Events New Scaler
Practice
Improve your coding skills with our resources
Contests
Compete in popular contests with top coders
Events
Attend free live masterclass hosted by top tech professionals
New
Scaler
Explore Offerings by SCALER

# Powerful Divisors

Problem Description

You are given an integer array A of length N.
For every integer X in the array, you have to find out the number of integers Y, such that 1 <= Y <= X, and the number of divisors of Y is a power of 2.

For example, 6 has the following divisors - [1, 2, 3, 6]. This is equal to 4, which is a power of 2.
On the other hand, 9 has the following divisors [1, 3, 9] which is 3, which is not a power of 2.

Return an array containing the answer for every X in the given array.

Problem Constraints
1 <= N <= 105
1 <= Amax <= 106
Sum of Amax over all test cases will not exceed 5 * 106

Input Format
The first argument is the integer array A.

Output Format
Return an array containing the answer for every X in the given array.

Example Input
Input 1:

A = [1, 4]

Input 2:

A = [5, 10]

Example Output
Output 1:

[1, 3]

Output 2:

[4, 8]

Example Explanation
Explanation 1:

The numbers 1, 2, 3 have the required number of divisors.

Explanation 2:

Only 4 and 9 are the numbers less than or equal to 10 which do not have the required number of divisors.

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
Hints
• Hint 1
• Solution Approach
• Complete Solution

## Discussion

Free Mock Assessment
Fill up the details for personalised experience.
All fields are mandatory
Current Employer *
Enter company name *
Select an option *
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
Phone Number *
OTP will be sent to this number for verification
+1 *
+1
Change Number
Phone Number *
OTP will be sent to this number for verification
+1 *
+1
Change Number
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
*Enter the expected year of graduation if you're student
Current Employer *
Company Name *