TotallyOriginallyCreatedByMe Conjecture

Consider segregating positive integers into two categories:

• Even-type : if its prime factorization has an even number of prime(s), or it equals to $1$ .

• Odd-type : if its prime factorization has an odd number of prime(s).

Define

• $E(N)$ to be the number of positive integers of even-type that are less than or equals to $N$

• $O(N)$ to be the number of positive integers of odd-type that are less than or equals to $N$

I claim that $E(N) \leq O(N)$ for all positive integers $N$ greater than $1$ but less than $10^9$ . Am I right?

Details and assumptions :

• $18 = 2 \times 3 \times 3$ , which has $3$ prime factors, so $18$ is an odd-type

• $19 = 19$ , which has $1$ prime factor, so $19$ is an odd-type

• $33 = 3 \times 11$ , which has $2$ prime factors, so $33$ is an even-type

• If $N=25$ , then $1,4,6,9,10,14,15,16,21,22,24,25$ are even-type , $2,3,5,7,8,11,12,13,17,18,19,20,23$ are odd-type . So $E(25)= 12, O(25)=13$ . Which means $E(25) \leq O(25)$ , thus it's true for $N=25$ .