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 A222711 #32 Jun 22 2024 12:33:21
%S A222711 1,3,12,14,15,35,105,190,248,357,616,812,1045,3080,3135,3339,4064,
%T A222711 5049,8323,8636,10659,12441,16065,19780,20026,23374,24871,29029,50065,
%U A222711 58435,64285,87685,124355,132957,137885,140335,248501,263055,317205,353133,423657,596037,655707,734517,894387
%N A222711 Numbers k such that gcd(sigma(k), phi(k)) (A009223) attains record values.
%C A222711 RECORDS transform of A009223.
%H A222711 Donovan Johnson, <a href="/A222711/b222711.txt">Table of n, a(n) for n = 1..500</a>
%H A222711 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a> (The RECORDS transform returns both the high-water marks and the places where they occur).
%t A222711 a[1] = 1; record = 1; a[n_] := a[n] = For[k = a[n-1] + 1, True, k++, g = GCD[DivisorSigma[1, k], EulerPhi[k]]; If[g > record, record = g; Return[k]]]; Table[a[n], {n, 1, 45}] (* _Jean-François Alcover_, Oct 07 2013 *)
%t A222711 DeleteDuplicates[Table[{k,GCD[DivisorSigma[1,k],EulerPhi[k]]},{k,900000}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Jun 22 2024 *)
%o A222711 (PARI) mg=0;for(x=1,1000000,g=A009223(x);if(g>mg,print1(x", ");mg=g))
%Y A222711 Cf. A009223, A222712.
%K A222711 nonn,nice
%O A222711 1,2
%A A222711 _Phil Carmody_, Mar 01 2013