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data/problems/342.yml

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---
:id: 342
:name: The totient of a square is a cube
:url: https://projecteuler.net/problem=342
:content: "Consider the number 50.  \n50<sup>2</sup> = 2500 = 2<sup>2</sup> × 5<sup>4</sup>,
  so φ(2500) = 2 × 4 × 5<sup>3</sup> = 8 × 5<sup>3</sup> = 2<sup>3</sup> × 5<sup>3</sup>.
  <sup>1</sup>  \nSo 2500 is a square and φ(2500) is a cube.\n\nFind the sum of all
  numbers n, 1 &lt n \\< 10<sup>10</sup> such that φ(n<sup>2</sup>) is a cube.\n\n<sup>1</sup>
  φ denotes **Euler's totient function**.\n\n"