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Omni-MATH / For positive integers n, let f(n) be the product of the digits of n. Find the largest positive integer m such that ∑_(n=1)^(∞)(f(n))/(m⌊log₁₀n⌋) is an integer.

Problem

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problem

For positive integers nn, let f(n)f(n) be the product of the digits of nn. Find the largest positive integer mm such that ∑n=1∞f(n)m⌊log10n⌋\sum_{n=1}^{\infty} \frac{f(n)}{m\left\lfloor\log _{10} n\right\rfloor} is an integer.
Plain-text mathematical notation (without MathML)
For positive integers n, let f(n) be the product of the digits of n. Find the largest positive integer m such that ∑_(n=1)^(∞)(f(n))/(m⌊log₁₀n⌋) is an integer.
Original LaTeX notation
For positive integers $n$, let $f(n)$ be the product of the digits of $n$. Find the largest positive integer $m$ such that $$\sum_{n=1}^{\infty} \frac{f(n)}{m\left\lfloor\log _{10} n\right\rfloor}$$ is an integer.

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Source and history

task_id
ce481e13-2610-509f-8c8f-223f5eb26868
task_key
test--ce481e13-2610-509f-8c8f-223f5eb26868
task_revision_id
1
config / split
/ test

Official source

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