von Mangoldt function

The Mangoldt function is the function defined by Λ(n) congruent {ln p | if n = p^k for p a prime 0 | otherwise, auto right match sometimes also called the lambda function. exp(Λ(n)) has the explicit representation e^(Λ(n)) = (LCM(1, 2, ..., n))/(LCM(1, 2, ..., n - 1)), where LCM(a, b, ...) denotes the least common multiple. The first few values of exp(Λ(n)) for n = 1, 2, ..., plotted above, are 1, 2, 3, 2, 5, 1, 7, 2, ... (OEIS A014963).

Bombieri's theorem | Chebyshev functions | explicit formula | greatest prime factor | lambda function | Landau's formula | least common multiple | least prime factor | Riemann function