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 A332515 #19 Dec 11 2024 06:38:51
%S A332515 15,16,20,24,25,30,33,44,50,51,64,66,68,69,80,87,92,96,102,116,120,
%T A332515 123,138,141,159,164,165,174,176,177,188,200,212,213,220,236,246,249,
%U A332515 255,256,264,267,272,275,282,284,289,300,303,318,320,321,330,332,339,340
%N A332515 Numbers k such that phi(k) == 8 (mod 12), where phi is the Euler totient function (A000010).
%C A332515 Dence and Pomerance showed that the asymptotic number of the terms below x is ~ c2 * x/sqrt(log(x)), where c2 = (sqrt(2*sqrt(3))/(3*Pi)) * c3^(-1/2) * (2*c3 - c4) = 0.3284176245..., 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 A332515 Amiram Eldar, <a href="/A332515/b332515.txt">Table of n, a(n) for n = 1..10000</a>
%H A332515 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 A332515 25 is a term since phi(25) = 20 == 8 (mod 12).
%t A332515 Select[Range[400], Mod[EulerPhi[#], 12] == 8 &]
%o A332515 (Magma) [k:k in [1..350]| EulerPhi(k) mod 12 eq 8]; // _Marius A. Burtea_, Feb 14 2020
%Y A332515 Cf. A000010, A017617, A175646, A332511, A332512, A332513, A332514, A332516.
%K A332515 nonn
%O A332515 1,1
%A A332515 _Amiram Eldar_, Feb 14 2020