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%I #13 Sep 08 2022 08:46:25
%S 13,21,26,28,35,36,37,39,42,45,52,56,57,61,63,65,70,72,73,74,76,77,78,
%T 84,90,91,93,95,97,99,104,105,108,109,111,112,114,117,119,122,124,126,
%U 129,130,133,135,140,143,144,146,147,148,152,153,154,155,156,157,161
%N Numbers k such that phi(k) == 0 (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 ~ x.
%H Amiram Eldar, <a href="/A332512/b332512.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 13 is a term since phi(13) = 12 == 0 (mod 12).
%t Select[Range[200], Divisible[EulerPhi[#], 12] &]
%o (Magma) [k:k in [1..170]| EulerPhi(k) mod 12 eq 0]; // _Marius A. Burtea_, Feb 14 2020
%Y Cf. A000010, A008594, A332511, A332513, A332514, A332515, A332516.
%K nonn
%O 1,1
%A _Amiram Eldar_, Feb 14 2020
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