this solution is wrong because of two reasons:

• the powers for each prime divisors are not necessarily the same
• I am describing the numbers of the form p*2²+q*3² instead of 2^2k3^2k

any other arguments in the post are flawed because of this.and mainly the fact that an arbitrary power can't really be expressed by the regex(except for hardcoded values like

(1{4}){9}/ means 36 but that's far from what is needed here )