Maths Olympiad Prep

Track / Stage 4 / 199 of 340 #459 of 1964

Problem 459

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

61. 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. Spacing, $ signs and \frac vs / are all fine.

Official solution

answer: 528

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.