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Q: Sum of perfect power till N

ShubhamSuppose there is a number k, then f(k) is the sum of all perfect powers that divides k. For a given N We need to find f(1) + f(2) + .... f(N). N can be upto 10^18. My solution is naive and cannot work for bigger N. Can someone suggest some formula for solving the problem.

The above question is now locked.
I wondered whether MO has at any point formulated some policy on questions from ongoing contest.
Maybe one could say that they are likely to be closed - since typically such questions are not research-level. But in my experience, many non-research-level questions are left open on MO.
On Mathematics moderators formulated a clear protocol what to do with such questions: “Contest problem” policy.
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Q: "Contest problem" policy

Willie WongWhat is our policy concerning contest questions on the Mathematics Stack Exchange? Why do we have a policy? What is a contest question? How we deal with on-going contest questions? I see a question that I know is from a contest, what do I do?

 

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