Arithmetic function
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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- enIn 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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- 1.50
- Has abstract
- enIn 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. There is a larger class of number-theoretic functions that do not fit the above definition, for example, the prime-counting functions. This article provides links to functions of both classes. Arithmetic functions are often extremely irregular (see ), but some of them have series expansions in terms of Ramanujan's sum.
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- enp/a013300
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- Arithmetic function
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- enArithmetic function
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- arxiv.org/PS_cache/arxiv/pdf/1103/1103.5861v2.pdf
- mathstat.carleton.ca/~williams/papers/pdf/249.pdf
- archive.org/details/introductiontoan00apos_0
- archive.org/details/modularfunctions0000apos
- www.mtholyoke.edu/~robinson/reu/reu05/rdineva1.pdf
- web.archive.org/web/20160305132124/https:/www.math.hmc.edu/~orrison/research/papers/totient.pdf
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- Additive function
- Arithmetic derivative
- Asymptotic analysis
- Average order of an arithmetic function
- Cambridge University Press
- Carmichael function
- Category:Arithmetic functions
- Category:Functions and mappings
- Cauchy product
- Chebyshev function
- Classification of discontinuities
- Completely additive function
- Completely multiplicative function
- Complex number
- Convergent series
- Convolution
- Coprime
- Cyclotomic field
- D. C. Heath and Company
- Dedekind psi function
- Differential operator
- Dirichlet character
- Dirichlet convolution
- Dirichlet series
- Discriminant
- Divisor function
- Divisor sum identities
- Divisor summatory function
- Eisenstein series
- Euler–Mascheroni constant
- Euler totient function
- Function (mathematics)
- Fundamental theorem of arithmetic
- Generating function
- Greatest common divisor
- Harmonic number
- Ideal class group
- Indicator function
- Jacobi symbol
- John Wiley & Sons
- Jordan totient function
- Kronecker symbol
- Lagrange's four-square theorem
- László Fejes Tóth
- Least common multiple
- Legendre symbol
- Liouville function
- Möbius function
- Möbius inversion
- Modular discriminant
- Modular form
- Modular function
- Multiplicative function
- Multiplicative group of integers modulo n
- Natural number
- Number theory
- Open interval
- P-adic valuation
- Partition function (number theory)
- Peter Gustav Lejeune Dirichlet
- P Kesava Menon
- Power series
- Prentice Hall
- Prime-counting function
- Prime factor
- Prime number
- Prime number theorem
- Prime omega function
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- Product rule
- Q-expansion
- Quadratic field
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- Ramanujan's sum
- Ramanujan tau function
- Riemann hypothesis
- Riemann zeta function
- Roots of unity
- Springer Nature
- Squarefree
- Subset
- Sum of squares function
- Undergraduate Texts in Mathematics
- Von Mangoldt function
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- SameAs
- Arithmetic function
- Aritmeettinen funktio
- Aritmetická funkce
- Aritmetická funkcia
- Aritmetična funkcija
- Aritmetika funkcio
- Aritmetisk funktion
- Fonction arithmétique
- Função aritmética
- Funció aritmètica
- Función aritmética
- Funkcja arytmetyczna
- Funzione aritmetica
- Hàm số học
- Heiltölufall
- m.01461
- Q140744
- QcBH
- Rekenkundige functie
- Számelméleti függvények
- Zahlentheoretische Funktion
- Арифметикалық функция
- Арифметическая функция
- Арифметична функція
- פונקציה אריתמטית
- تابع حسابی
- دالة حسابية
- അങ്കഗണിതഫലനം
- 数論的関数
- 算術函數
- 수론적 함수
- Subject
- Category:Arithmetic functions
- Category:Functions and mappings
- Text
- enΩ = a1 + a2 + ... + ak.
- enω = k,
- Title
- enArithmetic function
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- Arithmetic function?oldid=1124022873&ns=0
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- Wikipage page ID
- 3170
- Wikipage revision ID
- 1124022873
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