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 A143189 #17 Jun 07 2025 08:19:40
%S A143189 1,2,8,11,17,29,38,43,47,67,68,71,73,74,86,89,95,101,103,107,109,116,
%T A143189 122,127,128,143,151,188,191,194,197,215,223,227,241,248,251,254,269,
%U A143189 277,283,302,305,317,323,332,349,359,368,371,373,397,403,409,410,433,452
%N A143189 Numbers k such that at least one of the following equations holds: phi(2*k-1) = phi(2*k), sigma(2*k-1) = sigma(2*k), tau(2*k-1) = tau(2*k).
%C A143189 Inspired by A134922.
%H A143189 Amiram Eldar, <a href="/A143189/b143189.txt">Table of n, a(n) for n = 1..10000</a>
%t A143189 a[n_] =
%t A143189 If[EulerPhi[2*n - 1] - EulerPhi[2*n] == 0, n,
%t A143189 If[DivisorSigma[1, 2*n - 1] - DivisorSigma[1, 2*n] == 0, n,
%t A143189 If[Length[Divisors[2*n - 1]] - Length[Divisors[2*n]] == 0, n, {}]]];
%t A143189 Flatten[Table[a[n], {n, 1, 400}]]
%o A143189 (PARI) isok(k) = {my(f1 = factor(2*k-1), f2 = factor(2*k)); eulerphi(f1) == eulerphi(f2) || sigma(f1) == sigma(f2) || numdiv(f1) == numdiv(f2);} \\ _Amiram Eldar_, Jun 07 2025
%Y A143189 Cf. A000005 (tau), A000010 (phi), A000203 (sigma), A134922.
%K A143189 nonn
%O A143189 1,2
%A A143189 _Roger L. Bagula_, Oct 17 2008
%E A143189 Name edited by _Amiram Eldar_, Jun 07 2025