Maths Olympiad Prep

Track / Stage 4 / 215 of 340 #475 of 1964

Problem 475

AMC 12 late, AIME early
Number theory Difficulty 4.8 Find the answer

The increasing sequence 2,3,5,6,7,10,11,⋯⋯2,3,5,6,7,10,11, \cdots \cdots, contains all positive integers that are neither perfect squares nor perfect cubes. The 500th term of this sequence is \qquad .

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

answer: 528

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.