Problem
Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
2^2=4, 23=8, 24=16, 25=32
3^2=9, 33=27, 34=81, 35=243
4^2=16, 43=64, 44=256, 45=1024
5^2=25, 53=125, 54=625, 55=3125
If they are then placed in numerical order, with any repetition removed, we get the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
Ask
I have the algorithm done, I try it with a=5, b=5 and it works fine, with the number 100 I get 422, I am not sure if it is correct since the problem tells me that it is not, but I do not detect any error, could you give me a hand?
Code
getPowers(100, 100);
Collections.sort(numbers);
System.out.println(numbers);
System.out.println(numbers.size());
}
static List<Integer> numbers = new ArrayList<>();
public static void getPowers(int a, int b){
double num = 0;
for (int i = 2; i <=a ; i++) {
for (int j = 2; j <=b; j++) {
num = Math.pow(i,j);
if (!numbers.contains((int)num)) numbers.add((int)num);
}
}
}