python - Fastest way to calculate the sum of LCM(i,j) when i and j go from 1 to k

Question

I need to calculate the sum of the lcm(i,j) when i and j go from 1 to k. k can be = to numbers as big as 10^10.

its like this : https://www.programmersought.com/article/86482143316/ but I need to do it in Python. This is the Equation

The way ive been doing is to use 2 for loops and calculate the lcm of i and j but it takes WAY too long. Thought there could be a faster mathematical way maybe.

Thank you

question from:https://stackoverflow.com/questions/65864487/fastest-way-to-calculate-the-sum-of-lcmi-j-when-i-and-j-go-from-1-to-k

Answer 1

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