This is totally weird, and I think I messed up in getting this, but it is
true. Could someone with a lot of time and a lot of patience and a big
calculator check this? Thanks.
1 = 1/(2²- 1) + 1/(2³ - 1) + 1/(2^4 - 1) + 1/(2^5 - 1) + ... + 1/(3² - 1) +
1/(3³ - 1) + 1/(3^4 - 1) + ... + 1/(5² - 1) + 1/(5³ - 1) + 1/(5^4 - 1) + ...
In other words, if set x contains integral powers, (2³, 3³, 2², etc....) and
x' is the set of integers minus set x. Then this says:
1 = sum(n=2 to n=infinity (sum( i=1 to i = infinity, 1/((x'i)^n - 1))))
please confirm!!
this is a side formula I found, while working with primes. Hope it is not to
off topic.
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