1800 followers problem

Calculus Level 5

\[\large \sum_{k=1}^{1800} \psi(k)\]

If the above sum can be expressed as \(aH_b-c\gamma-d\) for some not necessarily distinct positive integers \(a,b,c\) and \( d\), evaluate \(a+b+c+d\) where \(b,c\) is maximum possible.

Notations:


This problem is original.
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