on the sum of the number of prime factors less then n

forgive the terminolegy

let p(n)=the number of prime factors

f(n)=sum from 2 to n of p(k)

then f(n) is o(nlogn) and nothing smaller

because the upper bound of p(k) is log2(n) therfor f(x) is defenetlly o(xlog2(x))

and sens from f(x) to f(x^2) we can take any number from thee list at f(x) multply it by another number from that list and get a number at(x^2)

we are gona get smallo(x^2) new numbers

therefor almost all of the numbers at f(x^2) are in f(x)*somthing which means there p(x) is bigger by at list 1

this is obviously a logarithmic growth

submitted by /u/atheist-projector
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Nevin Manimala

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