Concepts3
∑MathIntermediate
Harmonic Lemma
The Harmonic Lemma says that the values of \lfloor n/i \rfloor only change about 2\sqrt{n} times, so you can iterate those value blocks in O(\sqrt{n}) instead of O(n).
#harmonic lemma#integer division trick#block decomposition+12
∑MathIntermediate
Multiplicative Functions
A multiplicative function is an arithmetic function f with f(mn) = f(m)f(n) whenever gcd(m, n) = 1.
#multiplicative function#dirichlet convolution#mobius function+12
∑MathIntermediate
Euler's Totient Function
Euler's Totient Function φ(n) counts how many integers from 1 to n are coprime with n.
#euler totient#phi function#coprime count+12