A341750 -id:A341750 - cp's OEIS frontend

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 93, 94, 96

Offset: 1

Amiram Eldar, Feb 18 2021

nonn

First differs from A080197 at n = 28.
Erdős et al. (2008) proved that the asymptotic density of numbers k such that gcd(k, phi(k)) > (log(log(k)))^u for a real number u > 0 is equal to exp(-gamma) * Integral_{t=u..oo} rho(t) dt, where rho(t) is the Dickman-de Bruijn function and gamma is Euler's constant (A001620). For this sequence u = 1, and therefore its asymptotic density is 1 - exp(-gamma) = 0.43854... (A227242).
There are only 8 cyclic numbers (A003277) in this sequence: 1, 2, 3, 5, 7, 11, 13, 15. All the other terms are in A060679. The first term of A060679 which is not in this sequence is 1622.

			16 is a term since gcd(16, phi(16)) = gcd(16, 8) = 8 > log(log(16)) = 1.0197...
17 is not a term since gcd(17, phi(17)) = gcd(17, 16) = 1 < log(log(17)) = 1.0414...

Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős, Florian Luca and Carl Pomerance, On the proportion of numbers coprime to a given integer, in: J.-M. De Koninck, A. Granville and F. Luca (eds.), Anatomy of Integers, AMS, 2008, pp. 47-64.
Wikipedia, Dickman function.

Cf. A000010, A001620, A003277, A009195, A060679, A080130, A227242, A341750.

Select[Range[100], GCD[#, EulerPhi[#]] > Log[Log[#]] &]

isok(k) = (k==1) || (gcd(k, eulerphi(k)) > log(log(k))); \\ Michel Marcus, Feb 19 2021

cp's OEIS Frontend

A341749 Numbers k such that gcd(k, phi(k)) > log(log(k)).

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