What is the mathematical relationship between the frequencies of musical notes that we perceive identical, but at different octaves?

Humans have a logarithmic perception of the majority of uncountable and some countable things. A₀, which is percieved as the basic note, has a frequency of 27.50 Hz. A₁=55 Hz, and A₂=110 Hz. You might notice that each time we increase the octave, we multiply the previous frequency by 2. Hence, the formula for the note A would be:      A_n=27.52ⁿ Hz If we check this, then A₇=27.5128=3520 Hz, which, if you check any sources, you will find is correct.