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Omni-MATH / Find the number of positive integers n satisfying ϕ(n)|n such that

Problem

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

problem

Find the number of positive integers nn satisfying ϕ(n)|n\phi(n) | n such that ∑m=1∞([nm]−[n−1m])=1992\sum_{m=1}^{\infty} \left( \left[ \frac nm \right] - \left[\frac{n-1}{m} \right] \right) = 1992 What is the largest number among them? As usual, ϕ(n)\phi(n) is the number of positive integers less than or equal to nn and relatively prime to n.n.
Plain-text mathematical notation (without MathML)
Find the number of positive integers n satisfying ϕ(n)|n such that
∑_(m=1)^(∞)([(n)/(m)]−[(n−1)/(m)])=1992
What is the largest number among them? As usual, ϕ(n) is the number of positive integers less than or equal to n and relatively prime to n.
Original LaTeX notation
Find the number of positive integers $n$ satisfying $\phi(n) | n$ such that
\[\sum_{m=1}^{\infty} \left( \left[ \frac nm \right] - \left[\frac{n-1}{m} \right]  \right) =  1992\]
What is the largest number among them? As usual, $\phi(n)$ is the number of positive integers less than or equal to $n$ and relatively prime to $n.$

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Source and history

task_id
ba0d5ee2-0d8f-5ee4-ac5e-092cc6f6d451
task_key
test--ba0d5ee2-0d8f-5ee4-ac5e-092cc6f6d451
task_revision_id
1
config / split
/ test

Official source

initial import