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Find the missing positive integers

Source: Austrian Mathematical Olympiad 2008 Problem 5

February 6, 2009
geometry3D geometrynumber theory unsolvednumber theory

Problem Statement

Which positive integers are missing in the sequence {an} \left\{a_n\right\}, with a_n \equal{} n \plus{} \left[\sqrt n\right] \plus{}\left[\sqrt [3]n\right] for all n≥1 n \ge 1? ([x] \left[x\right] denotes the largest integer less than or equal to x x, i.e. g g with g \le x < g \plus{} 1.)
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