I have the Fermat Factorizations of $n = pq$ where $p$ and $q$ are primes. I am trying to find a formula/pattern for the number of cycles required to perform the factorization in terms of $n, p, q$. Here is a set of integers I have interated over:
FermatFactorization(15) (5)(3) NumCycles: 1 FermatFactorization(21) (7)(3) NumCycles: 2 FermatFactorization(33) (11)(3) NumCycles: 5 FermatFactorization(35) (7)(5) NumCycles: 1 FermatFactorization(39) (13)(3) NumCycles: 6 FermatFactorization(51) (17)(3) NumCycles: 9 FermatFactorization(55) (11)(5) NumCycles: 3 FermatFactorization(57) (19)(3) NumCycles: 11 FermatFactorization(65) (13)(5) NumCycles: 4 FermatFactorization(69) (23)(3) NumCycles: 14 FermatFactorization(77) (11)(7) NumCycles: 2 FermatFactorization(85) (17)(5) NumCycles: 7 FermatFactorization(87) (29)(3)
Can you find the formula for the given data as described above?