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Statements

Subject Item
dbr:Multiplicative_function
rdfs:label
Multiplicative function
rdfs:comment
In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1) = 1 and whenever a and b are coprime. An arithmetic function f(n) is said to be completely multiplicative (or totally multiplicative) if f(1) = 1 and f(ab) = f(a)f(b) holds for all positive integers a and b, even when they are not coprime.
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dbc:Multiplicative_functions
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dbr:Unique_factorization_domain dbr:Euler_product dbr:Divisor_function dbr:Principal_ideal_domain dbr:Indicator_function dbr:Legendre_symbol dbr:0 dbr:Bell_series dbr:Square-free_element dbr:Square-free_integer dbr:Additive_function dbr:Dirichlet_character dbr:Greatest_common_divisor dbr:Dirichlet_convolution dbr:Least_common_multiple dbr:Number_theory dbr:Liouville_function dbr:Negative_number dbr:Complex_number dbr:Coprime_integers dbr:List_of_zeta_functions dbr:Finite_field dbr:Ramanujan_tau_function dbr:Unit_function dbr:Prime_number dbr:Dirichlet_series dbr:Möbius_function dbr:Lambert_series dbr:Möbius_inversion_formula dbr:Sign_(mathematics) dbr:On-Line_Encyclopedia_of_Integer_Sequences dbc:Multiplicative_functions dbr:Euler's_totient_function dbr:Identity_element dbr:Fundamental_theorem_of_arithmetic dbr:Divisor dbr:Identity_function dbr:Completely_multiplicative_function dbr:Homomorphism dbr:Arithmetic_function dbr:Integer dbr:Monoid dbr:Abelian_group
dbo:abstract
In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1) = 1 and whenever a and b are coprime. An arithmetic function f(n) is said to be completely multiplicative (or totally multiplicative) if f(1) = 1 and f(ab) = f(a)f(b) holds for all positive integers a and b, even when they are not coprime.
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n13:Multiplicative_function