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 A385562 #9 Jul 05 2025 11:25:03
%S A385562 1,2,4,6,12,18,22,24,30,42,60,66,72,78,84,90,114,120,150,156,180,198,
%T A385562 210,300,330,390,420,510,546,570,600,630,750,780,840,966,990,1122,
%U A385562 1170,1200,1260,1410,1470,1560,1596,1620,1650,1680,1806,1830,1890,1980,2100
%N A385562 Numbers m such that (1/m) * Sum_{k=1..m} k/phi(k) sets a record value, where phi is the Euler totient function (A000010).
%C A385562 Limit_{m->oo} (1/m) * Sum_{k=1..m} k/phi(k) = zeta(2)*zeta(3)/zeta(6) (A082695) (Sitaramachandrarao, 1985; Sándor et al., 2005). This sequence is infinite if this mean converges to the limit only from below.
%D A385562 József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 29.
%H A385562 Amiram Eldar, <a href="/A385562/b385562.txt">Table of n, a(n) for n = 1..1752</a> (terms below 10^10)
%H A385562 R. Sitaramachandrarao, <a href="https://www.jstor.org/stable/44236939">On an error term of Landau. II</a>, The Rocky Mountain Journal of Mathematics, Vol. 15, No. 2 (1985), pp. 579-588.
%t A385562 seq[lim_] := Module[{s = {}, sum = 0, rm = 0, r}, Do[sum += k/EulerPhi[k]; r = sum/k; If[r > rm, rm = r; AppendTo[s, k]], {k, 1, lim}]; s]; seq[2500]
%o A385562 (PARI) list(lim) = {my(sm = 0, rm = 0, r); for(k = 1, lim, sm += k/eulerphi(k); r = sm/k; if(r > rm, rm = r; print1(k, ", ")));}
%Y A385562 Cf. A000010, A068885, A069947, A082695, A330899, A385561.
%K A385562 nonn
%O A385562 1,2
%A A385562 _Amiram Eldar_, Jul 03 2025