Carmichael function

Summary

Carmichael function is an arithmetic function^[1]. It draws 170 Wikipedia views per month (arithmetic_function category, ranking #1 of 4).^[2]

Key Facts

• Carmichael function's instance of is recorded as arithmetic function^[3].
• Robert Daniel Carmichael is named after Carmichael function^[4].
• Carmichael function's Commons category is recorded as Carmichael function^[5].
• Carmichael function's Freebase ID is recorded as /m/04f405^[6].
• Carmichael function's defining formula is recorded as \lambda(n)=\exp(\mathbb Z/(n))^\times^[7].
• Carmichael function's defining formula is recorded as \begin{align}\lambda(2^n) & =\begin{cases} \phi(2^n) & n=0,1,2 \ \phi(2^n)/2 & n\ge3 \end{cases} \\lambda(p^n) & =\phi(p^n)\qquad(p\in\mathbb P\setminus{2},\;n\in\mathbb Z^+) \\lambda(p_1^{n_1}\cdots p_k^{n_k}) & =\operatorname{lcm}{\lambda(p_1^{n_1}),\dots,\lambda(p_k^{n_k})}\qquad(p_1,\dots,p_k\in\mathbb P,\;n_1,\dots n_k\in\mathbb Z^+,\;p_i\ne p_j,\;i\ne j)\end{align}^[8].
• Carmichael function's MathWorld ID is recorded as CarmichaelFunction^[9].
• Carmichael function's Quora topic ID is recorded as Carmichael-Function^[10].
• Carmichael function's maintained by WikiProject is recorded as WikiProject Mathematics^[11].
• Carmichael function's Microsoft Academic ID is recorded as 173948734^[12].
• Carmichael function's in defining formula is recorded as \lambda^[13].
• Carmichael function's in defining formula is recorded as \exp^[14].
• Carmichael function's in defining formula is recorded as (-)^\times^[15].
• Carmichael function's in defining formula is recorded as \mathbb Z^[16].
• Carmichael function's in defining formula is recorded as /^[17].
• Carmichael function's in defining formula is recorded as (n)^[18].
• Carmichael function's in defining formula is recorded as \phi^[19].
• Carmichael function's in defining formula is recorded as \mathbb P^[20].
• Carmichael function's in defining formula is recorded as \operatorname{lcm}^[21].

Why It Matters

Carmichael function draws 170 Wikipedia views per month (arithmetic_function category, ranking #1 of 4).^[2] It has Wikipedia articles in 14 language editions, a strong signal of global cultural recognition.^[22] It is known by 6 alternative names across languages and contexts.^[23]