A332514 - OEIS

A332514

Numbers k such that phi(k) == 6 (mod 12), where phi is the Euler totient function (A000010).

%I #13 Sep 08 2022 08:46:25

%S 7,9,14,18,19,27,31,38,43,49,54,62,67,79,81,86,98,103,127,134,139,151,

%T 158,162,163,199,206,211,223,243,254,271,278,283,302,307,326,331,343,

%U 361,367,379,398,422,439,446,463,486,487,499,523,542,547,566,571,607,614

%N Numbers k such that phi(k) == 6 (mod 12), where phi is the Euler totient function (A000010).

%C Dence and Pomerance showed that the asymptotic number of the terms below x is ~ (3/8) * x/log(x).

%H Amiram Eldar, <a href="/A332514/b332514.txt">Table of n, a(n) for n = 1..10000</a>

%H Thomas Dence and Carl Pomerance, <a href="https://doi.org/10.1007/978-1-4757-4507-8_2">Euler's function in residue classes</a>, in: K. Alladi, P. D. T. A. Elliott, A. Granville and G. Tenebaum (eds.), Analytic and Elementary Number Theory, Developments in Mathematics, Vol. 1, Springer, Boston, MA, 1998, pp. 7-20, <a href="https://math.dartmouth.edu/~carlp/PDF/paper116.pdf">alternative link</a>.

%e 19 is a term since phi(19) = 18 == 6 (mod 12).

%t Select[Range[600], Mod[EulerPhi[#], 12] == 6 &]

%o (Magma) [k:k in [1..650]| EulerPhi(k) mod 12 eq 6]; // _Marius A. Burtea_, Feb 14 2020

%Y Cf. A000010, A017593, A332511, A332512, A332513, A332515, A332516.

%K nonn

%O 1,1

%A _Amiram Eldar_, Feb 14 2020