No prime power exists since there are no duplicate prime numbers in the prime factorization.
3 x 37 = 111
111 = 37 x 3
3 x 37 = 111
111 3,37 3 x 37 = 111
111 = 31 x 371
111 = 31 x 371
111 = 31 x 371
Divide by three. 3 x 37 = 111
51*111 = 55
22 x 111 = 44
23 x 111 = 88