Wow, this one is the most clever solution I have seen up to date

Nice. For those confused why this works, see my solution: it has some comments to explain it.

As others pointed out, you should set a lower bound for a to avoid unnecessary computations.

It can become faster by changing range as well as make only one rule for if, proof is my solution
Good Coding

This could run much faster if you replace starting point of a by: n/sqrt(2). Easily provable.

Thanks! I completely forgot that you can get the summation of an integer series through a formula!

Total is the sum of all the number between 1 and n!
Yes, it is important to compute Total even if you use another approach to solve the problem as the sum of all the number between a,b (with b > a) will be total(n=b) - total(n=a). It is mainly the solution of a summation of a integer serie.

what does the variable total represent and why is it important in the solution?

don't forget the spoiler tag (I just added it to your comment)

is_ingerger() is userful.

卧槽

as long as i undersatand the priciple of the "and" "or" . i think i can do this @@

niubility

its second line just ....complex ....