Apumerghata

Apumerghata is an operation. It comes from the Gujarati words "અપૂર્ણાંક (apūrṇāṅka)", "ઉમેરો (umērō)", and "ઘાત (ghāta)", meaning "fraction", "add", and "exponent", respectively.

'''Note: This page is outdated. I recently made a new version of this operation, with a completely new formula.'''

Symbol
Its symbol is four dots.

Formula
The formula for apumerghata is n = $${(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n})^\sqrt[n]{n}}$$.

Numbers from 1-20 using apumerghata
Note: 1 is the only rational number in this sequence. Every number afterwards is irrational. I could try and go higher, maybe up to 1,000,000, but that would take hours, days, weeks, even months, to calculate it manually.