What is the growth rate of the 2nd Chebyshev function i.e. $Ψ(x)$
where $Ψ(x)$ $=$ $ln(lcm(1, 2, ... , x)$
$ln$ denotes the natural logarithm and $lcm(1, 2, ... , x)$ refers to the lowest common multiple of all integers from 1 to x or alternatively we can say LCM of first x integers.
More specifically I am working on an inequality so I want the growth rate of the function $F(x)$ $=$ $| Ψ(x) - x |$
Growth rate can be big O or little o notation or simply the degree of growth.
Source: [1] https://en.wikipedia.org/wiki/Chebyshev_function [2] https://mathworld.wolfram.com/ChebyshevFunctions.html
Note - I have tried to search for it on the internet including on MSE but could not find any relevant information. I don't have much experience in this field, just asking out of curiosity, thus sorry and thanks in advance.