query: Deduce the number of divisors, $d(n)$ is multiplicative and obtain a formula of $d(n)$ in terms of prime decomposition
positive_passages.docid: 148796
positive_passages.text: Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$
negative_passages.docid: 102086
negative_passages.text: Prove a property of divisor function
negative_passages.docid: 10920
negative_passages.text: $\delta_2(n)$ the sum of the squares of the positive divisors of $n$.
negative_passages.docid: 52157
negative_passages.text: Prove that $d(n)\leq 2\sqrt{n}$
negative_passages.docid: 75733
negative_passages.text: Divisibility of prime numbers
negative_passages.docid: 41614
negative_passages.text: Formula for prime counting function
negative_passages.docid: 150185
negative_passages.text: Let $d=GCD(n^2+5,n^3-5n^2+6n)$ show that $d|630$
negative_passages.docid: 53263
negative_passages.text: Show $\sum\limits_{d|n}\phi(d) = n$.
negative_passages.docid: 31555
negative_passages.text: Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
negative_passages.docid: 79940
negative_passages.text: $\binom{p}{i}$ divisible by $p$, with $p$ prime
negative_passages.docid: 102398
negative_passages.text: Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative
negative_passages.docid: 49509
negative_passages.text: A number $n$ has $12$ divisors and $d_{d_4-1} = (d_1+d_2+d_4)d_8$.
negative_passages.docid: 75516
negative_passages.text: Relatively Prime Numbers and Number of Divisors of n
negative_passages.docid: 48251
negative_passages.text: Prove that if $n \in \mathbb{N}$, then $\sum_{d|n}{(d(n))^3}=(\sum_{d|n}{d(n)})^2$ where $d(n)$ is the divisor function.
negative_passages.docid: 133528
negative_passages.text: $\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$
negative_passages.docid: 86051
negative_passages.text: Find the sum of reciprocals of divisors given the sum of divisors
negative_passages.docid: 139833
negative_passages.text: Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.