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Does $2r - \sigma(r)$ divide $\sigma(r)$ if $r$ is deficient-perfect?

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#number-theory #divisibility #divisor-sum #arithmetic-functions #perfect-numbers
27
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Does $\gcd(r, \sigma(r)) = 2r - \sigma(r)$ always hold when $r$ is deficient-perfect?

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#divisibility #gcd-and-lcm #divisor-sum #arithmetic-functions #perfect-numbers
147
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Arithmetic Sequence Word Problem with floor heights

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#sequences-and-series #arithmetic-progressions #arithmetic-functions
101
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An interesting identity involving the abundancy index of divisors of odd perfect numbers

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#ordinary-differential-equations #number-theory #divisor-sum #arithmetic-functions #perfect-numbers
84
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How to prove that $\sigma_{k+1}(n) = \sum\limits_{d|n}d^k \cdot\phi(d)\cdot\sigma_{k}(\frac{n}{d})$

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#number-theory #totient-function #divisor-sum #arithmetic-functions #dirichlet-convolution
102
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Finding root for the segment - found the formula but it doesn't work for some values - wrong formula?

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#linear-algebra #algebra-precalculus #analytic-geometry #roots #arithmetic-functions
3.7k
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Question about $T_n = n + (n-1)(n-2)(n-3)(n-4)$

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#sequences-and-series #arithmetic-functions
953
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Intuitive basis of Mobius inversion?

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#intuition #analytic-number-theory #arithmetic-functions #mobius-inversion #dirichlet-convolution
150
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Farey Sequence Vector Orthogonality Relation Question

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#number-theory #vector-spaces #arithmetic-functions #farey-sequences
1.6k
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What's the meaning of this $(m,n) = 1$

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#notation #arithmetic-functions
352
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Relation between Dirichlet convolution and Bell series and convolution of functions and the Fourier transform?

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#fourier-analysis #analytic-number-theory #convolution #arithmetic-functions #dirichlet-convolution
127
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Arithmetic progressions that generate an infinite number of powers of 2?

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#elementary-number-theory #arithmetic-functions
412
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Help with $\sum_{d\mid n}τ(d)^2=\sum_{d \mid n}τ(d)^3$

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#elementary-number-theory #summation #arithmetic-functions
606
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Euler phi function: $\sum_{n=1}^{N}\sum_{d\mid n}d\cdot\phi(d)$

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#number-theory #summation #totient-function #arithmetic-functions
49
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Mean of given Arithmetic function

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#statistics #arithmetic-functions

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