Given the partial sum function

nChebyshevPsi[x_] := Sum[MangoldtLambda[y], {y, x}] 

I would like a True response from

AsymptoticEqual[nChebyshevPsi[x], x, x -> Infinity]

considering that this is a well established fact in Number Theory.

My PC, however, seems to be in an infinite loop...

Is there anyway to speed this up? Or otherwise show this with Mathematica?

See also: Table of Chebyshev psi function


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