f(1) = 1
f(2) = 2
f(p) = 2
f(4) = 4
f(6) = 4
f(8) = 6
f(9) = 5
f(10) = 4
f(12) = 8
f(14) = 4
f(15) = 4
f(16) = 10
f(18) = 10
f(20) = 8

f(pq) =?= f(p)f(q)
f(p_1^q_1p_2^q_2...) =?= f(p_1^q_1)f(p_2^q_2)...
f(p^q) = 2(1+...+p^floor(q/2))      (q mod 2 = 1)
f(p^q) = 2(1+...+p^(q/2-1))+p^(q/2) (q mod 2 = 0)

