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Omni-MATH / For a positive integer n, let d(n) be the number of positive divisors of n, and let φ(n) be the number of positive integers not exceeding n which are coprime to n. Does there exist…

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For a positive integer nn, let d(n)d(n) be the number of positive divisors of nn, and let φ(n)\varphi(n) be the number of positive integers not exceeding nn which are coprime to nn. Does there exist a constant CC such that φ(d(n))d(φ(n))≤C \frac {\varphi ( d(n))}{d(\varphi(n))}\le C for all n≥1n\ge 1 [i]Cyprus[/i]
Plain-text mathematical notation (without MathML)
For a positive integer n, let d(n) be the number of positive divisors of n, and let φ(n) be the number of positive integers not exceeding n which are coprime to n. Does there exist a constant C such that

(φ(d(n)))/(d(φ(n)))≤C
for all n≥1

[i]Cyprus[/i]
Original LaTeX notation
For a positive integer $n$, let $d(n)$ be the number of positive divisors of $n$, and let $\varphi(n)$ be the number of positive integers not exceeding $n$ which are coprime to $n$. Does there exist a constant $C$ such that

$$ \frac {\varphi ( d(n))}{d(\varphi(n))}\le C$$
for all $n\ge 1$

[i]Cyprus[/i]

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Source and history

task_id
c27c568f-27ec-51b5-9fa7-210bc1de39c1
task_key
test--c27c568f-27ec-51b5-9fa7-210bc1de39c1
task_revision_id
1
config / split
/ test

Official source

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