WebNov 28, 2024 · Your stated interest is in co-prime pairs (a, b). The carefree couple adds an additional restriction that a is square-free. Therefore it is not the same problem, though … In number theory, the totient summatory function $${\displaystyle \Phi (n)}$$ is a summatory function of Euler's totient function defined by: $${\displaystyle \Phi (n):=\sum _{k=1}^{n}\varphi (k),\quad n\in \mathbf {N} }$$It is the number of coprime integer pairs {p, q}, 1 ≤ p ≤ q ≤ n. See more Using Möbius inversion to the totient function, we obtain Φ(n) has the asymptotic expansion where ζ(2) is the See more • Arithmetic function See more • Totient summatory function • Decimal expansion of totient constant product(1 + 1/(p^2*(p-1))), p prime >= 2) See more

nt.number theory - Computing the Mertens function - MathOverflow

WebApr 1, 2024 · Our first result gives an asymptotic formula for the summatory function of any balanced Jordan totient quotient J e (n), which implies that J e (n) is constant on average. Theorem 1. Let r ∈ N, e = (e 1, …, e r) ∈ Z r be a vector of integers, and J e be a Jordan totient quotient of weight w = ∑ i i e i = 0. エキゾテラ

Totient summatory function - OeisWiki

WebSummation Function for Euler's Totient Function. is a summatory function of Euler's totient function defined by: It is the number of coprime integer pairs {p, q}, 1 p q n. WebThe lower and upper bounds are found for the leading term of summatory totient function P k≤N k uφv(k) in various ranges of u ∈ Rand v ∈ Z. Keywords: Summatory totient functions, … Webwhere φis the Euler’s totient function, and (k,n) denotes the greatest common divisor of k and n. ... and an asymptotic formula for its summatory function. Motivated and inspired … エキゾチック 猫