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MATH / For positive integer n such that n<10,000, the number n+2005 has exactly 21 positive factors. What is the sum of all the possible values of n?

Problem

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problem

For positive integer nn such that n<10,000n < 10{,}000, the number n+2005n+2005 has exactly 21 positive factors. What is the sum of all the possible values of nn?
Plain-text mathematical notation (without MathML)
For positive integer n such that n<10,000, the number n+2005 has exactly 21 positive factors. What is the sum of all the possible values of n?
Original LaTeX notation
For positive integer $n$ such that $n < 10{,}000$, the number $n+2005$ has exactly 21 positive factors. What is the sum of all the possible values of $n$?

level

Level 5

type

Number Theory

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Source and history

task_id
d1aaf1af-5310-5317-b850-f6034deef178
task_key
number~5ftheory--test--d1aaf1af-5310-5317-b850-f6034deef178
task_revision_id
1
config / split
number_theory / test

Official source

initial import