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The largest subset of a finite cartesian product in which distinct elements differ in at least 2 components

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#combinatorics #number-theory #cyclotomic-polynomials #divisor-counting-function
150
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Prove or disprove: $ \sum_{b \vee d = x} \tau(b) \tau(d) = \tau(x)^3$

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#elementary-number-theory #summation #least-common-multiple #divisor-counting-function
311
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A $q$-continued fraction connected to the divisor function?

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#continued-fractions #theta-functions #q-series #divisor-counting-function
3.3k
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A natural number has exactly 10 divisors including 1 and itself.How many distinct prime factors can this natural number have?

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#elementary-number-theory #proof-verification #prime-numbers #divisibility #divisor-counting-function
143
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Injective function? Find a formula? Factors

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#elementary-number-theory #functions #divisor-counting-function
229
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From $\prod_{d\mid n}d=n^{\sigma_0(n)/2}$ to $n!=\operatorname{lcm}(1,\ldots,n)^{e(n)}$, where $\sigma_0(n)$ is the number of divisors

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#number-theory #proof-verification #asymptotics #least-common-multiple #divisor-counting-function
255
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Is the asymptotic growth rate of the product of divisor function up to $n$ known?

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#number-theory #asymptotics #divisor-counting-function
26
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What is the intuitive idea behind this claim on the divisor function?

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#number-theory #divisor-counting-function
64
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Counting divisors of a number

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#combinatorics #elementary-number-theory #arithmetic-functions #multiplicative-function #divisor-counting-function
672
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Average number of square free divisors for $n\leq x$

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#number-theory #asymptotics #riemann-zeta #divisor-counting-function
39
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Working with divisors

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#elementary-number-theory #divisibility #divisor-sum #divisor-counting-function
122
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The Diophantine Equation $m(n-2016)=n^{2016}$

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#algebra-precalculus #elementary-number-theory #diophantine-equations #prime-factorization #divisor-counting-function
148
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When the Sum of digits exceed the Number of Divisors

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#elementary-number-theory #divisor-counting-function
97
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$\sigma _{0}(n)=\sigma _{0}(n+1)$ will occur infinitely often.

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#number-theory #analytic-number-theory #divisor-counting-function
53
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A function related to divisior counting function

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#number-theory #asymptotics #analytic-number-theory #divisor-counting-function

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