This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332513 #18 Dec 11 2024 06:38:05
%S A332513 5,8,10,12,17,29,32,34,40,41,48,53,55,58,60,75,82,85,88,89,100,101,
%T A332513 106,110,113,115,125,128,132,136,137,145,149,150,160,170,173,178,184,
%U A332513 187,192,197,202,204,205,226,230,232,233,235,240,250,253,257,265,269,274
%N A332513 Numbers k such that phi(k) == 4 (mod 12), where phi is the Euler totient function (A000010).
%C A332513 Dence and Pomerance showed that the asymptotic number of the terms below x is ~ c1 * x/sqrt(log(x)), where c1 = (sqrt(2*sqrt(3))/(3*Pi)) * c3^(-1/2) * (2*c3 + c4) = 0.6109136202..., c3 = Product_{primes p == 2 (mod 3)} (1 + 1/(p^2-1)), and c4 = Product_{primes p == 2 (mod 3)} (1 - 1/(p+1)^2).
%H A332513 Amiram Eldar, <a href="/A332513/b332513.txt">Table of n, a(n) for n = 1..10000</a>
%H A332513 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. Tenenbaum (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 A332513 17 is a term since phi(17) = 16 == 4 (mod 12).
%t A332513 Select[Range[300], Mod[EulerPhi[#], 12] == 4 &]
%o A332513 (Magma) [k:k in [1..300]| EulerPhi(k) mod 12 eq 4]; // _Marius A. Burtea_, Feb 14 2020
%Y A332513 Cf. A000010, A017569, A175646, A332511, A332512, A332514, A332515, A332516.
%K A332513 nonn
%O A332513 1,1
%A A332513 _Amiram Eldar_, Feb 14 2020