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Proving identity using Dirichlet L functions

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#totient-function #arithmetic-functions #dirichlet-series #mobius-function #dirichlet-convolution
75
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What is meant by $\sum_{d \le x}f(d)$ in this equation?

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#summation #notation #divisor-sum #arithmetic-functions #dirichlet-series
297
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A total function is representable iff it is weakly representable

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#logic #definition #first-order-logic #proof-theory #arithmetic-functions
191
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About the characterization of solutions of an equation that involves particular values of the Dedekind psi function

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#elementary-number-theory #divisibility #arithmetic-functions
118
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Why does the divisor-counting function appear in bounds for Kloosterman sums?

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#analytic-number-theory #arithmetic-functions #multiplicative-function
41
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Summation of certain divisible numbers

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#totient-function #arithmetic-functions #mobius-function #coprime
154
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An identity of Arithmetic Functions

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#number-theory #elementary-number-theory #arithmetic-functions
59
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if such counter example to Lehmer's totient problem exists then could we have more counter examples?

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#arithmetic-functions #primality-test #lucas-lehmer-test
272
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On the equation $\psi(-1+2(\psi(n)-n))=n$ involving the Dedekind psi function, as a characterization of Mersenne primes

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#elementary-number-theory #prime-numbers #divisibility #arithmetic-functions #mersenne-numbers
94
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Calculating k-th Dirichlet root of invertible arithmetic function

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#number-theory #elementary-number-theory #arithmetic-functions
71
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Reference request - Online copy of T. N. Sinha's "Note on perfect numbers"?

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#number-theory #elementary-number-theory #reference-request #arithmetic-functions #perfect-numbers
62
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Euler function-Fermat's small theorem

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#arithmetic #totient-function #arithmetic-functions
61
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Euler function theorem

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#totient-function #arithmetic-functions
119
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A formula for $D(x)D(y) - D(xy)$ in terms of the sum-of-aliquot-divisors function, when $\gcd(x,y)=1$

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#algebra-precalculus #elementary-number-theory #closed-form #arithmetic-functions
96
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Does $k=1$ follow from $I(5^k)+I(m^2) \leq \frac{43}{15}$, if $p^k m^2$ is an odd perfect number with special prime $p=5$?

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#number-theory #conjectures #divisor-sum #arithmetic-functions #perfect-numbers

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