benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / To every natural number k,k≥2, there corresponds a sequence a_(n)(k) according to the following rule: a₀=k, a_(n)=τ(a_(n−1)) ∀n≥1, in which τ(a) is the number of different divisors…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

To every natural number k,k≥2k, k \geq 2, there corresponds a sequence an(k)a_n(k) according to the following rule: a0=k,an=τ(an−1)∀n≥1,a_0 = k, \qquad a_n = \tau(a_{n-1}) \quad \forall n \geq 1, in which τ(a)\tau(a) is the number of different divisors of aa. Find all kk for which the sequence an(k)a_n(k) does not contain the square of an integer.
Plain-text mathematical notation (without MathML)
To every natural number k,k≥2, there corresponds a sequence a_(n)(k) according to the following rule:
a₀=k, a_(n)=τ(a_(n−1)) ∀n≥1,
in which τ(a) is the number of different divisors of a. Find all k for which the sequence a_(n)(k) does not contain the square of an integer.
Original LaTeX notation
To every natural number $k, k \geq 2$, there corresponds a sequence $a_n(k)$ according to the following rule:
\[a_0 = k, \qquad a_n = \tau(a_{n-1})  \quad \forall n \geq 1,\]
in which $\tau(a)$ is the number of different divisors of $a$. Find all $k$ for which the sequence $a_n(k)$ does not contain the square of an integer.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
e786a0e1-7eb1-5e70-9733-e9b5979a29ea
task_key
test--e786a0e1-7eb1-5e70-9733-e9b5979a29ea
task_revision_id
1
config / split
/ test

Official source

initial import