The Mertens function is the summary function M(n) congruent sum_(k = 1)^n μ(k), where μ(n) is the Möbius function. The first few values are 1, 0, -1, -1, -2, -1, -2, -2, -2, -1, -2, -2, ... (OEIS A002321). M(n) is also given by the determinant of the n×n Redheffer matrix. Values of M(10^n) for n = 0, 1, 2, ... are given by 1, -1, 1, 2, -23, -48, 212, 1037, 1928, -222, ... (OEIS A084237).

Mertens conjecture | Möbius function | Redheffer matrix | squarefree

Franz Carl Joseph Mertens