A073087 -id:A073087 - cp's OEIS frontend

A091456 Least number k such that n * phi(k) < k, where phi is Euler's totient function.

2, 6, 30, 210, 30030, 223092870, 13082761331670030, 3217644767340672907899084554130, 1492182350939279320058875736615841068547583863326864530410

Offset: 1

Robert G. Wilson v, Jan 10 2004

nonn

By Mertens' theorem and the Prime Number Theorem log log a(n) ~ n / e^gamma. - Charles R Greathouse IV, Sep 07 2012

Amiram Eldar, Table of n, a(n) for n = 1..13

Subsequence of A002110.

Cf. A000010, A005579, A054741, A073087, A091439 (n * phi(k) <= k).

a(n) = {k = 1; while (n*eulerphi(k) >= k, k++); k;} \\ Michel Marcus, Sep 25 2013

a(n)=my(k=1);forprime(p=2,,if(n*eulerphi(k)Charles R Greathouse IV, Sep 25 2013

a(n) = A002110(A005579(n)). - Amiram Eldar, Nov 30 2024

A164347 The n-th term is the minimum number x such that x/Totient(x) >= n.

Original entry on oeis.org

2, 2, 6, 30, 210, 30030, 223092870, 13082761331670030, 3217644767340672907899084554130

Offset: 1

Fred Schneider, Aug 13 2009

These numbers are all primorials. Primorials necessarily must be the minimum terms in this sequence (given the nature of Euler's Totient function).

Essentially the same as A091456. - R. J. Mathar, Aug 17 2009

			2 => 2/totient(2) = 2 (so it is both the first and 2nd entry of the sequence).
30 => 30/totient(30) = 15/4 >= 3.
210 => 210/totient(210) = 210/48 >= 4.

Wikipedia, Euler's totient function

Each number n in this sequence is of the form: primorial(x). A164348, the related sequence, contains the x's.

Cf. A073087, A091456.

cp's OEIS Frontend

A091456 Least number k such that n * phi(k) < k, where phi is Euler's totient function.

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