benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Does there exist a sequence of positive integers a₁,a₂,... such that every positive integer occurs exactly once and that the number τ(na_(n+1)^(n)+(n+1)a_(n)^(n+1)) is divisible by…

Problem

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

problem

Does there exist a sequence of positive integers a1,a2,...a_1,a_2,... such that every positive integer occurs exactly once and that the number τ(nan+1n+(n+1)ann+1)\tau (na_{n+1}^n+(n+1)a_n^{n+1}) is divisible by nn for all positive integer. Here τ(n)\tau (n) denotes the number of positive divisor of nn.
Plain-text mathematical notation (without MathML)
Does there exist a sequence of positive integers a₁,a₂,... such that every positive integer occurs exactly once and that the number τ(na_(n+1)^(n)+(n+1)a_(n)^(n+1)) is divisible by n for all positive integer.

Here τ(n) denotes the number of positive divisor of n.
Original LaTeX notation
Does there exist a sequence of positive integers $a_1,a_2,...$ such that every positive integer occurs exactly once and that the number $\tau (na_{n+1}^n+(n+1)a_n^{n+1})$ is divisible by $n$ for all positive integer.

Here $\tau (n)$ denotes the number of positive divisor of $n$.

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
7269e6bf-8d2e-5c02-b8f3-3b2db5100276
task_key
test--7269e6bf-8d2e-5c02-b8f3-3b2db5100276
task_revision_id
1
config / split
/ test

Official source

initial import