19 lines
831 B
Markdown
19 lines
831 B
Markdown
Euler's Totient function, `phi(n)` (sometimes called the phi function),
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is used to determine the number of numbers less than n which are relatively prime to n.
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For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, `phi(9)=6`.
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n | Relatively Prime | phi(n) | n/phi(n)
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---|------------------|--------|-------
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2 | 1 | 1 | 2
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3 | 1,2 | 2 | 1.5
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4 | 1,3 | 2 | 2
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5 | 1,2,3,4 | 4 | 1.25
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6 | 1,5 | 2 | 3
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7 | 1,2,3,4,5,6 | 6 | 1.1666...
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8 | 1,3,5,7 | 4 | 2
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9 | 1,2,4,5,7,8 | 6 | 1.5
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10 | 1,3,7,9 | 4 | 2.5
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It can be seen that n=6 produces a maximum `n/phi(n)` for `n <= 10`.
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Find the value of `n <= 1,000,000` for which `n/phi(n)` is a maximum. |