Omni-MATH / Given a fixed positive integer a≥9. Prove: There exist finitely many positive integers n, satisfying: (1)τ(n)=a (2)n|ϕ(n)+σ(n) Note: For positive integer n, τ(n) is the number of p…

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Given a fixed positive integer a≥9. Prove: There exist finitely many positive integers n, satisfying:
(1)τ(n)=a
(2)n|ϕ(n)+σ(n)
Note: For positive integer n, τ(n) is the number of positive divisors of n, ϕ(n) is the number of positive integers ≤n and relatively prime with n, σ(n) is the sum of positive divisors of n.

Given a fixed positive integer $a\geq 9$. Prove: There exist finitely many positive integers $n$, satisfying:
(1)$\tau (n)=a$
(2)$n|\phi (n)+\sigma (n)$
Note: For positive integer $n$, $\tau (n)$ is the number of positive divisors of $n$, $\phi (n)$ is the number of positive integers $\leq n$ and relatively prime with $n$, $\sigma (n)$ is the sum of positive divisors of $n$.

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task_id

50943f23-f067-5e58-b322-f1d136bd22cd

task_key

test--50943f23-f067-5e58-b322-f1d136bd22cd

task_revision_id

3

config / split

/ test

Official source

initial import