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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(N)} \sum_{n=1}^{N} \frac{1}{\varphi(n)} = \frac{\zeta\!\left(2\right) \zeta\!\left(3\right)}{\zeta\!\left(6\right)}
TeX:
\lim_{N \to \infty} \frac{1}{\log(N)} \sum_{n=1}^{N} \frac{1}{\varphi(n)} = \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(n) Limiting value of sequence
Loglog(z)\log(z) Natural logarithm
Sumnf(n)\sum_{n} f(n) Sum
Totientφ(n)\varphi(n) 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)), For(n, 1, N))), For(N, Infinity)), Div(Mul(RiemannZeta(2), RiemannZeta(3)), RiemannZeta(6)))))

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2020-08-27 09:56:25.682319 UTC