CUBEFR  Cube Free Numbers
A cube free number is a number who’s none of the divisor is a cube number (A cube number is a cube of a integer like 8 (2 * 2 * 2) , 27 (3 * 3 * 3) ). So cube free numbers are 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18 etc (we will consider 1 as cube free). 8, 16, 24, 27, 32 etc are not cube free number. So the position of 1 among the cube free numbers is 1, position of 2 is 2, 3 is 3 and position of 10 is 9. Given a positive number you have to say if its a cube free number and if yes then tell its position among cube free numbers.
Input
First line of the test case will be the number of test case T (1 <= T <= 100000) . Then T lines follows. On each line you will find a integer number n (1 <= n <= 1000000).
Output
For each input line, print a line containing “Case I: ”, where I is the test case number. Then if it is not a cube free number then print “Not Cube Free”. Otherwise print its position among the cube free numbers.
Example
Sample Input: 10 1 2 3 4 5 6 7 8 9 10 Sample Output: Case 1: 1 Case 2: 2 Case 3: 3 Case 4: 4 Case 5: 5 Case 6: 6 Case 7: 7 Case 8: Not Cube Free Case 9: 8 Case 10: 9
hide comments
Subhendu Sethi:
20160521 03:04:32
No need to Prime Factorize. Think about sieving! Easy. 

mohitgupta07:
20160513 22:36:02
dun knw why getting wrong answer _ can anyone tell me dat how many cube free no.s lie in this range!!


ysn:
20160502 15:04:45
@Sarthak Munshi 9 is a perfect square not a cube number. you are confusing addition with multiplication. 3+3+3=9 is not a cube number but 3*3*3=27 is a cube number.


Sarthak Munshi:
20160502 12:09:30
How can 18 be a cube free number ? 9 is a divisor of 18 and it is a cube . 

ysn:
20160412 13:38:29
@Muhammad Ridowan i wrote a code that doesnt even use a loop. but still i am getting TimeLimit exceeded. Why?


ALi Ibrahim:
20160410 22:26:35
My 50th on Spoj :D 

pvsmpraveen:
20160129 20:03:39
Cutest lowerbound ever 

aakash_s:
20160107 20:19:24
The same code in my compiler gave memory overflow ...when i realized there was none other option....i submitted and AC 0.03s 

sy_117:
20151023 20:41:23
Nice ques. learnt somthing new !!!!!


prakash_reddy:
20151005 19:33:38
My 100th on Spoj.... prime factorization roxxxxxxxx.... :) 
Added by:  Muhammad Ridowan 
Date:  20110614 
Time limit:  0.100s1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own. For alternate thanks Sayef Azad Sakin 