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Square of number of divisors of n equals n

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#number-theory #divisibility #divisor-sum #divisor-counting-function
34
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Given $n\in\mathbb N$ what are the maximum number of divisors of a natural number not more than $n$?

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#number-theory #prime-factorization #divisor-counting-function
119
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Average Number of Small Divisors

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#number-theory #analytic-number-theory #divisor-sum #fractional-part #divisor-counting-function
128
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What is $\sum_{n=2}^{\infty} \frac{d(n)}{n(n-1)} $?

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#sequences-and-series #generating-functions #analytic-number-theory #divisor-counting-function
100
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Approximation for the number of unordered $k$-factorizations of positive integer $n$

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#number-theory #analytic-number-theory #arithmetic-functions #divisor-counting-function
82
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Some questions about the arithmetic function $\,g(n)=\sum_{(k,n)=1}\tau(k)$

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#number-theory #prime-numbers #arithmetic-functions #divisor-counting-function
194
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The function $ g(n)=\sum_{\substack {1\lt k\leq n \\ \gcd(k,n)=1}}d(k-1)$

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#combinatorics #number-theory #totient-function #arithmetic-functions #divisor-counting-function
649
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What is the formula to calculate the number of divisors of $n!$

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#factorial #divisor-counting-function
131
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Can $\sum_{k=1}^n \arctan(\cot(\frac{\pi n}{k}))$ be simplified?

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#trigonometry #summation #divisor-counting-function
232
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If we know about the divisors of $n$, what can we comment about the divisors of $n+x$?

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#number-theory #elementary-number-theory #algebraic-number-theory #divisor-sum #divisor-counting-function
69
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Can this divisor and floor function be calculated faster

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#combinatorics #divisor-sum #divisors-algebraic-geometry #divisor-counting-function
100
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What does the notation $\sum_{d\mid (k,n)}$ mean?

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#summation #notation #binomial-coefficients #divisor-counting-function
109
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If $n=2^{10}\times 3^5$. Find number of divisors of $n^2$ which are less than $n$ but do not divide $n$

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#elementary-number-theory #divisor-counting-function
122
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Count the number of integer solutions to $x_1+x_2+x_3+x_4+x_5+x_6=25$ when, $x_1,x_2,x_3$ are odd and $x_4,x_5,x_6$ are even and $x_i is N$

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#combinatorics #discrete-mathematics #diophantine-equations #divisor-counting-function
39
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Count the Number of Positive Integer Solutions to $\prod_{i=1}^{k}x_i\le N$

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#combinatorics #elementary-number-theory #algorithms #divisor-counting-function

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