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I would like to compute a general $n$-term of a sequence $$ 1, 5, 12, 24, 37, 61, 80, \dots$$ However I do not understand what $\phi$ refers to in the formula at $$\sum_{k=1}^n \phi(k)\lfloor n/k \rfloor^2$$

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up vote 4 down vote accepted

It's the Euler totient function.

$\varphi(n)$ is the number of integers between 1 and $n$ that have no common factors with $n$. For example, $\varphi(9) = 6$, because 1, 2, 4, 5, 7, and 8 have no common factors with 9.

Wikipedia should have a lot of discussion. If you need a good introduction, any book on elementary number theory will contain one, and there is a section in Concrete Mathematics by Graham, Knuth, and Patashnik.

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