arithmetical function where stands for Dirichlet convolution. Miscellaneous Let m and n be distinct, odd, and positive. Then the Jacobi symbol satisfies the law of quadratic reciprocity: Let D(n) be the arithmetic derivative. Then the logarithmic derivative See Arithmetic derivative for details. Let λ(n) be Liouville's function. Then and Let λ(n) be Carmichael's function. Then Further, See Multiplicative group of integers modulo n and Primitive root modulo n. Note that Compare this with where τ(n) is Ramanujan's function. First 100 values of some arithmetic functions Notes References Further reading External links Matthew Holden, Michael Orrison, Michael Varble Yet another Generalization of Euler's Totient Function Huard, Ou, Spearman, and Williams. Elementary Evaluation of Certain Convolution Sums Involving Divisor Functions Dineva, Rosica, The Euler Totient, the Möbius, and the Divisor Functions László Tóth, Menon's Identity and arithmetical sums representing functions of several variables Functions and mappings