About: Arithmetic function

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In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n". An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n.

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rdf:type	Thing
rdfs:label	Arithmetic function (en)
rdfs:comment	In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n". An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n. (en)
sameAs	Arithmetic function Arithmetic function
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Subject	Arithmetic functions Functions and mappings
Link from a Wikipage to an external page	https://arxiv.org/PS_cache/arxiv/pdf/1103/1103.5861v2.pdf https://web.archive.org/web/20160305132124/https:/www.math.hmc.edu/~orrison/research/papers/totient.pdf http://mathstat.carleton.ca/~williams/papers/pdf/249.pdf https://archive.org/details/introductiontoan00apos_0 https://archive.org/details/modularfunctions0000apos http://www.mtholyoke.edu/~robinson/reu/reu05/rdineva1.pdf
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Wikipage page ID	3170 (xsd:integer)
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Wikipage revision ID	1064355858 (xsd:integer)
Link from a Wikipage to another Wikipage	Greatest common divisor Möbius function Möbius inversion formula Number theory Product rule Root of unity Sum of squares function Undergraduate Texts in Mathematics Wiley (publisher) World Scientific Additive function Arithmetic derivative Asymptotic analysis Average order of an arithmetic function Von Mangoldt function Cambridge University Press Carmichael function Arithmetic functions Cauchy product Generating function Jacobi symbol Jordan's totient function Functions and mappings Differential operator Dirichlet character Dirichlet convolution Dirichlet series Discriminant Divisor function Divisor sum identities Divisor summatory function Legendre symbol P-adic order P Kesava Menon Peter Gustav Lejeune Dirichlet Power series Quadratic field Quadratic reciprocity Chebyshev function Classification of discontinuities Cyclotomic field D. C. Heath and Company Dedekind psi function Liouville function Prentice Hall Prime-counting function Prime number Prime number theorem Prime omega function Prime power Primitive root modulo n Springer Nature Square-free integer Complex number Convergent series Convolution Coprime integers Eisenstein series Partition function (number theory) Completely multiplicative function Function (mathematics) Fundamental theorem of arithmetic Ideal class group Indicator function Harmonic number Interval (mathematics) Kronecker symbol

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