# Fungrim entry: 9923b7

$\lim_{N \to \infty} \frac{1}{\log(N)} \sum_{n=1}^{N} \frac{1}{\varphi(n)} = \frac{\zeta\!\left(2\right) \zeta\!\left(3\right)}{\zeta\!\left(6\right)}$
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
SequenceLimit$\lim_{n \to a} f(n)$ Limiting value of sequence
Log$\log(z)$ Natural logarithm
Sum$\sum_{n} f(n)$ Sum
Totient$\varphi(n)$ Euler totient function
Infinity$\infty$ Positive infinity
RiemannZeta$\zeta\!\left(s\right)$ 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)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC