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Fungrim entry: 9923b7

limN1log ⁣(N)n=1N1φ ⁣(n)=ζ ⁣(2)ζ ⁣(3)ζ ⁣(6)\lim_{N \to \infty} \frac{1}{\log\!\left(N\right)} \sum_{n=1}^{N} \frac{1}{\varphi\!\left(n\right)} = \frac{\zeta\!\left(2\right) \zeta\!\left(3\right)}{\zeta\!\left(6\right)}
TeX:
\lim_{N \to \infty} \frac{1}{\log\!\left(N\right)} \sum_{n=1}^{N} \frac{1}{\varphi\!\left(n\right)} = \frac{\zeta\!\left(2\right) \zeta\!\left(3\right)}{\zeta\!\left(6\right)}
Definitions:
Fungrim symbol Notation Short description
SequenceLimitlimnaf ⁣(n)\lim_{n \to a} f\!\left(n\right) Limiting value of sequence
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Infinity\infty Positive infinity
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Source code for this entry:
Entry(ID("9923b7"),
    Formula(Equal(SequenceLimit(Mul(Div(1, Log(N)), Sum(Div(1, Totient(n)), Tuple(n, 1, N))), N, Infinity), Div(Mul(RiemannZeta(2), RiemannZeta(3)), RiemannZeta(6)))))

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2019-08-17 11:32:46.829430 UTC