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?