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 A065389 #24 Mar 22 2025 04:42:21
%S A065389 1,3,5,7,11,13,17,19,25,29,31,37,43,53,61,73,97,109,127,143,151,157,
%T A065389 181,211,241,313,331,337,397,403,421,527,541,601,631,661,757,779,899,
%U A065389 1009,1147,1201,1321,1333,1517,1621,1763,1801,2017,2161,2341,2501,2521
%N A065389 Numbers m such that sigma(phi(m)) sets a new record, i.e., sigma(phi(m)) > sigma(phi(k)) for all k < m numbers.
%C A065389 Numbers m at which A000203(A000010(m)) = A062402(m) reaches a new maximal value.
%H A065389 Amiram Eldar, <a href="/A065389/b065389.txt">Table of n, a(n) for n = 1..958</a> (terms below 10^11; terms 1..500 from Harry J. Smith)
%e A065389 A062402 begins {1, 1, 3, 3, 7, 3, 12, 7, 12, 7, 18, 7, 28, 12, 15, 15, 31, 12, 39, 15, 28, 18, 36, 15, 42}. New peaks are reached at positions 3, 5, 7, 11, 13, 17, 19, 25. These peak values are 3, 7, 12, 18, 28, 31, 39, 42, respectively.
%t A065389 a=0; s=0; Do[s=DivisorSigma[1, EulerPhi[n]]; If[s>a, a=s; Print[n]], {n, 1, 10000}];
%t A065389 DeleteDuplicates[Table[{n,DivisorSigma[1,EulerPhi[n]]},{n,2600}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Jul 20 2023 *)
%o A065389 (PARI) { n=r=0; for (m=1, 10^9, x=sigma(eulerphi(m)); if (x > r, r=x; write("b065389.txt", n++, " ", m); if (n==500, return)) ) } \\ _Harry J. Smith_, Oct 18 2009
%Y A065389 Cf. A000010, A000203, A062402, A065390, A065391, A065392, A065393, A065294.
%K A065389 nonn
%O A065389 1,2
%A A065389 _Labos Elemer_, Nov 05 2001