Ayn Rand definitely moved away from Nietzsche (as they are very different), but I think it's hard to deny his influence on her. Some parallels, particularly her idea of the ubermensch, are very Nietzschean (though again, the actual definition of the two differ markedly). To really understand where she's coming from, and where she's getting her ideas (which are often better and more deeply explored elsewhere) you have to read other philosophy. Nietzsche is one, perhaps Aristotle is another.
As for my allegation of Rand's hate for Objectivists, it looks like I misremembered. It was actually Libertarians who Rand despised, not Objectivists.[1]
You are talking from ignorance. She doesn't have an "idea of the Ubermensch" - she esteems honest ordinary men highly, and condemns modern elites.
What is Nietzsche's solution to the problem of universals? What does he say about the is-ought problem? What does he say about capitalism and individual rights? All of these things are discussed in Rand, none are discussed in Nietzsche, who rejects reason, logic and universal truths.
Sure, read other philosophy, but to really really understand where she's coming from, you have to read her, and not confidently spout second-hand misinformation.
Rand is most known for her "virtue of selfishness" idea and her high esteem if not worship of people who she considers to be superior due to their daring, individuality, flaunting of social conventions, and self-centeredness. This is a dumbed down or "mini me" version of Nietzsche's ubermensch concept.
Rand is not known for her view on any is-ought problem or her views on universals. She may have something to say about them, perhaps it's even original in some manner, but it's generally not what most Objectivists and Libertarians flock to her for. They flock to her to get some philosophical approval for their own self-centerdness. To those people I again recommend they read Nietzsche, to learn what one of the most influential philosophers of all time though on this subject that Rand tried to co-opt.
I never claimed and do not claim that everything Rand ever thought was thought first by Nietzsche, but the central idea that she's known for and that she championed she got (in a very distorted way) from him.
I also never suggested that Rand should not be read. It is a pity that she is ignored in academia. As a result, most of Rand's fans are often effectively isolated from the rest of the philosophical community and wallow in an intellectual backwater, with little awareness that there are other philosophers, what they thought, or how Rand's ideas relate to them. It would be much better if her work was read, taught, engaged, and challenged in academia, and her place in place in philosophical history was made more overt.
Finally, I have read Rand. Not nearly as much as her fans would have me read, I'm sure. But enough to say what I say from first-hand experience.
As for my allegation of Rand's hate for Objectivists, it looks like I misremembered. It was actually Libertarians who Rand despised, not Objectivists.[1]
[1] - http://aynrandlexicon.com/ayn-rand-ideas/ayn-rand-q-on-a-on-...