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Omni-MATH / For a positive integer n, denote by τ(n) the number of positive integer divisors of n, and denote by ϕ(n) the number of positive integers that are less than or equal to n and relat…

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problem

For a positive integer nn, denote by τ(n)\tau(n) the number of positive integer divisors of nn, and denote by ϕ(n)\phi(n) the number of positive integers that are less than or equal to nn and relatively prime to nn. Call a positive integer nn good if φ(n)+4τ(n)=n\varphi(n)+4 \tau(n)=n. For example, the number 44 is good because φ(44)+4τ(44)=44\varphi(44)+4 \tau(44)=44. Find the sum of all good positive integers nn.
Plain-text mathematical notation (without MathML)
For a positive integer n, denote by τ(n) the number of positive integer divisors of n, and denote by ϕ(n) the number of positive integers that are less than or equal to n and relatively prime to n. Call a positive integer n good if φ(n)+4τ(n)=n. For example, the number 44 is good because φ(44)+4τ(44)=44. Find the sum of all good positive integers n.
Original LaTeX notation
For a positive integer $n$, denote by $\tau(n)$ the number of positive integer divisors of $n$, and denote by $\phi(n)$ the number of positive integers that are less than or equal to $n$ and relatively prime to $n$. Call a positive integer $n$ good if $\varphi(n)+4 \tau(n)=n$. For example, the number 44 is good because $\varphi(44)+4 \tau(44)=44$. Find the sum of all good positive integers $n$.

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Source and history

task_id
0eef69c5-fce3-504b-b01d-7d75967b89bf
task_key
test--0eef69c5-fce3-504b-b01d-7d75967b89bf
task_revision_id
1
config / split
/ test

Official source

initial import