benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / For any integer n, define ⌊n⌋ as the greatest integer less than or equal to n. For any positive integer n, let f(n)=⌊n⌋+⌊(n)/(2)⌋+⌊(n)/(3)⌋+⋯+⌊(n)/(n)⌋. For how many values of …

Problem

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

problem

For any integer nn, define ⌊n⌋\lfloor n\rfloor as the greatest integer less than or equal to nn. For any positive integer nn, let f(n)=⌊n⌋+⌊n2⌋+⌊n3⌋+⋯+⌊nn⌋.f(n)=\lfloor n\rfloor+\left\lfloor\frac{n}{2}\right\rfloor+\left\lfloor\frac{n}{3}\right\rfloor+\cdots+\left\lfloor\frac{n}{n}\right\rfloor. For how many values of n,1≤n≤100n, 1 \leq n \leq 100, is f(n)f(n) odd?
Plain-text mathematical notation (without MathML)
For any integer n, define ⌊n⌋ as the greatest integer less than or equal to n. For any positive integer n, let f(n)=⌊n⌋+⌊(n)/(2)⌋+⌊(n)/(3)⌋+⋯+⌊(n)/(n)⌋. For how many values of n,1≤n≤100, is f(n) odd?
Original LaTeX notation
For any integer $n$, define $\lfloor n\rfloor$ as the greatest integer less than or equal to $n$. For any positive integer $n$, let $$f(n)=\lfloor n\rfloor+\left\lfloor\frac{n}{2}\right\rfloor+\left\lfloor\frac{n}{3}\right\rfloor+\cdots+\left\lfloor\frac{n}{n}\right\rfloor.$$ For how many values of $n, 1 \leq n \leq 100$, is $f(n)$ odd?

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
27730c2e-5b87-50fc-b566-2d465532525f
task_key
test--27730c2e-5b87-50fc-b566-2d465532525f
task_revision_id
1
config / split
/ test

Official source

initial import