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11A25 - Number theory :: Elementary number theory :: Arithmetic functions; related numbers; inversion formulas

$2^{\omega(n)} \le \tau(n) \le 2^{\Omega(n)}$ owned by Wkbj79 $\sigma$ function owned by CompositeFan $\tau$ function owned by Wkbj79 additive function owned by Wkbj79 aliquot sequence owned by PrimeFan all positive integers are polite numbers except powers of two owned by PrimeFan alternate proof of Möbius inversion formula owned by rm50 another proof that a number is polite iff it is positive and not a positive power of owned by CWoo applications of second order recurrence relation formula owned by Wkbj79 arithmetic function owned by mathcam arithmetic functions form a ring owned by rm50 Basel problem owned by PrimeFan Basel problem derivation owned by curious Bombieri-Vinogradov theorem owned by Mravinci Brocard's problem owned by PrimeFan Carmichael function owned by PrimeFan character of a finite group owned by alozano completely multiplicative functions whose convolution inverses are completely multiplicative owned by Wkbj79 composition of multiplicative functions owned by Wkbj79 convolution inverses for arithmetic functions owned by Wkbj79 criterion for a multiplicative function to be completely multiplicative owned by Wkbj79 Dirichlet character owned by bbukh the divisor function is multiplicative owned by yark divisor sum of an arithmetic function owned by azdbacks4234 elementary results about multiplicative functions and convolution owned by Wkbj79 Euler phi at a product owned by pahio Euler phi function owned by Wkbj79 every positive integer greater than 30 has at least one composite totative owned by mps examples of aliquot sequences owned by PrimeFan examples of characteristic functions owned by Wkbj79 examples of perfect totient numbers owned by PrimeFan existence of square roots of non-negative real numbers owned by PrimeFan formula for the convolution inverse of a completely multiplicative function owned by Wkbj79 if $\mu(n) = (-1)^{\omega(n)}$ then $\tau(n) = 2^{\omega(n)}$ owned by 1and2and4 impractical number owned by PrimeFan iterated sum of divisors function owned by PrimeFan iterated totient function owned by CompositeFan Liouville function owned by KimJ Mangoldt function owned by KimJ Mertens conjecture owned by PrimeFan Mertens function owned by CompositeFan Mertens' first theorem owned by KimJ method for representing rational numbers as sums of unit fractions using practical numbers owned by PrimeFan multiplicative function owned by Wkbj79 Möbius function owned by mps Möbius inversion owned by mathcam Nicomachus' theorem owned by PrimeFan non-multiplicative function owned by Mathprof noncototient owned by PrimeFan nonprincipal real characters $\mod p$ are unique owned by rm50 nontotient owned by PrimeFan number of (nondistinct) prime factors function owned by Wkbj79 number of distinct prime factors function owned by CompositeFan parity of $\tau$ function owned by pahio perfect totient number owned by CompositeFan pointwise multiplication of a completely multiplicative function distibutes over convolution owned by Wkbj79 polite number owned by PrimeFan power of two owned by 1and2and4 practical number owned by CompositeFan practical number owned by mathcam prime counting function owned by XJamRastafire prime difference function owned by XJamRastafire product of divisors function owned by pahio proof of all positive integers are polite numbers except powers of two owned by n847530 proof of square root of square root binomial owned by rspuzio proof of the correspondence between even 2-superperfect numbers and Mersenne primes owned by PrimeFan proof that exceeds the product of the primes up to owned by PrimeFan proof that $\tau(n)$ is the number of positive divisors of owned by Wkbj79 proof that 3 is the only prime perfect totient number owned by PrimeFan proof that all powers of 3 are perfect totient numbers owned by PrimeFan proof that Euler $\varphi$ function is multiplicative owned by Wkbj79 proof that the sum of the iterated totient function is always odd owned by PrimeFan Pólya's conjecture owned by PrimeFan Ramanujan tau function owned by Wkbj79 refactorable number owned by CompositeFan relationship between totatives and divisors owned by Wkbj79 sparsely totient number owned by PrimeFan square root owned by Wkbj79 square root of 2 owned by MathNerd square root of 3 owned by PrimeFan square root of 5 owned by MathNerd square root of square root binomial owned by pahio square roots of rationals owned by pahio sum of $\frac{\mu(n)}{n}$ owned by mathcam Sun's conjecture on sums of primes and triangular numbers owned by PrimeFan superperfect number owned by CompositeFan table of continued fractions of $\sqrt{n}$ for owned by PrimeFan table of differences between $\lceil \sqrt{n!} \rceil^2$ and for owned by PrimeFan table of polite number representations for owned by PrimeFan table of values of the Liouville function and its summatory function owned by PrimeFan table of values of the Möbius function and the Mertens function owned by PrimeFan the sum of the values of a character of a finite group is owned by alozano totative owned by CompositeFan totient owned by mathcam totient valence function owned by CompositeFan triangular number counting function owned by PrimeFan uniqueness of Moebius function owned by mathcam values of and $\displaystyle \prod_{i = 1}^{\pi(n)} p_i$ for owned by PrimeFan values of for which $\varphi(n)=\tau(n)$ owned by Wkbj79 Zeisel number owned by CompositeFan zero owned by Mravinci
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