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Number of integers for which $\Omega=k$

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#elementary-number-theory #analytic-number-theory #arithmetic-functions
83
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Is there a number $\mathscr{D}_2 \neq \mathscr{D} = {{3003}^2}\cdot{22021}$ satisfying a certain condition?

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#number-theory #inequality #divisor-sum #arithmetic-functions #perfect-numbers
340
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Attempt to get a characterization of even perfect numbers from an equation involving the Dedekind psi function

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#elementary-number-theory #divisibility #conjectures #arithmetic-functions #perfect-numbers
202
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Prove that for every $ϵ>0$ there exist infinitely many natural numbers $n$, such that $τ(n)\geq 2^{(1-ϵ)(\log(n)/\log(\log(n))}$.

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#number-theory #analytic-number-theory #arithmetic-functions
141
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On odd perfect numbers and a GCD - Part II

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#number-theory #gcd-and-lcm #divisor-sum #arithmetic-functions #perfect-numbers
135
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When does $\gcd(m,\sigma(m^2))$ equal $\gcd(m^2,\sigma(m^2))$? What are the exceptions?

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#number-theory #elementary-number-theory #gcd-and-lcm #divisor-sum #arithmetic-functions
36
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Show this congruence holds

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#elementary-number-theory #divisibility #primitive-roots #arithmetic-functions
304
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A question about Dirichlet series

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#analytic-number-theory #riemann-zeta #arithmetic-functions #dirichlet-series
286
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Dirichlet Series in analytic number theory

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#analytic-number-theory #arithmetic-functions #dirichlet-series
172
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Functions that link to divisor function

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#number-theory #functions #arithmetic-functions #divisor-counting-function
268
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If an arithmetic function $f$ satisfies $f(mn) \leq f(m)f(n)$ (whenever $\gcd(m,n)=1$), is $f$ weakly multiplicative or submultiplicative?

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#terminology #gcd-and-lcm #divisor-sum #arithmetic-functions #multiplicative-function
197
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Can this inequality involving the deficiency and sum of aliquot divisors be improved?

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#number-theory #elementary-number-theory #upper-lower-bounds #divisor-sum #arithmetic-functions
91
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Showing that $\sum_{m=1}^{n}{\sigma(m)}=\sum_{k=1}^{n}{k\cdot \left\lfloor \frac n k\right\rfloor}$

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#elementary-number-theory #solution-verification #arithmetic-functions
118
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Finding $f$ with Möbius inversion formula

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#elementary-number-theory #arithmetic-functions #mobius-inversion
194
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Why is this arbitrary-looking identity of arithmetic functions "obvious"?

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#number-theory #analytic-number-theory #alternative-proof #arithmetic-functions

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