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IMC 2013/1/5

Source: Imc 2013 Problem 5

August 8, 2013
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Problem Statement

Does there exist a sequence (an)\displaystyle{\left( {{a_n}} \right)} of complex numbers such that for every positive integer p\displaystyle{p} we have that ∑n=1+∞anp\displaystyle{\sum\limits_{n = 1}^{ + \infty } {a_n^p} } converges if and only if p\displaystyle{p} is not a prime?
Proposed by Tomáš Bárta, Charles University, Prague.
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