What does 一番 mean in 与5年前相比翻了一番? In the following sentence:


  调查显示，32%的海外民众认为中国是对世界经济影响最大的国家。与5年前相比翻了一番。


一番 might mean "one time" (at least my dictionary on macOS says "一倍" while Pleco only lists "one kind"). However, 翻 I believe means "double" as a verb here.

So I feel that the sentence is contradictionary... At least from the context, the influence of China would be "doubled". But then what is the meaning of 一番 here?
翻（了）n番 is common phrase, meaning 2^n. For example, 翻一番 = 2, 翻两番 = 4， ....

But the interesting phrase is 翻n倍. Some would take 翻n倍 = 翻n番, and some would take 翻n倍 = 1*n, and some take 翻n倍 = 1*(n+1). For example, 50翻3倍 could be 150, 400 or 200. This is really a moot point. Personally, I would take 翻n倍 = 1*(n+1) and 50翻3倍 would be 200.