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Cancellations in partial sum of Ramanujan tau function

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#complex-analysis #number-theory #analytic-number-theory #arithmetic-functions
88
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On composite solutions of $\operatorname{rad}(n-1)=\operatorname{rad}(\varphi(n))$

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#sequences-and-series #elementary-number-theory #reference-request #totient-function #arithmetic-functions
151
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Truncated Euler's sigma function

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#elementary-number-theory #arithmetic-functions
76
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Partial summation $\sum_{p\leq X}a_p$ via $\sum_{n\leq X}a_n\Lambda(n)$.

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#number-theory #analytic-number-theory #arithmetic-functions
581
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Long list of values of Ramanujan Tau function

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#number-theory #analytic-number-theory #arithmetic-functions #analytic-functions
88
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Mysterious multiplicative function?

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#number-theory #arithmetic-functions #dirichlet-convolution
132
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Show that $\sigma(n)$ is equally often even and odd

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#number-theory #divisor-sum #arithmetic-functions #multiplicative-function #parity
1.4k
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"I am sure there are infinitely many perfect numbers"

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#number-theory #divisor-sum #arithmetic-functions #perfect-numbers
231
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Modular Forms: With special congruences!

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#number-theory #modular-arithmetic #fourier-transform #modular-forms #arithmetic-functions
203
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On arithmetic functions whose Dirichlet series has a special kind of abscissa of absolute convergence

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#analytic-number-theory #arithmetic-functions #dirichlet-series #multiplicative-function #dirichlet-convolution
62
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On Uniform Elementary Estimates of Arithmetic Sums Error Term

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#elementary-number-theory #arithmetic-functions #dirichlet-series
79
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Upper and lower density of the set of natural numbers whose sum of positive divisors is a perfect square

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#number-theory #analytic-number-theory #divisor-sum #arithmetic-functions
82
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Show that the quotient $\frac{\sigma(p^3)}{\tau(p^3)}$ is an integer for $p$ prime

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#elementary-number-theory #divisor-sum #arithmetic-functions #divisor-counting-function
45
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Compare $\sum_{k=1}^n k^{\operatorname{rad}\left(\lfloor\frac{n}{k}\rfloor\right)}$ and $\sum_{k\mid n}k^{\operatorname{rad}\left(\frac{n}{k}\right)}$

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#sequences-and-series #asymptotics #analytic-number-theory #prime-factorization #arithmetic-functions
108
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What does $(-1)^{2/3}$ equal?

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#arithmetic #arithmetic-functions

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