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 A335318 #9 May 31 2020 21:57:11
%S A335318 1,6,140,270,672,8190,30240,332640,14303520,17428320,27027000,
%T A335318 191711520,2144862720,3506025600,5943057120,14378364000,45578332800,
%U A335318 288662774400,505159855200,2020639420800,10680522652800,54557264361600
%N A335318 Harmonic numbers (A001599) k with a record abundancy index sigma(k)/k.
%C A335318 The corresponding record values are 1, 2, 2.4, 2.666..., 3, 3.2, 4, 4.363..., ...
%C A335318 The terms 1, 6, 672 and 30240 are multiply perfect numbers (A007691) with abundancy indices 1, 2, 3, and 4, respectively. There is no 5-multiperfect number (A046060) in this sequence since A046060(1) = 14182439040 is larger than the harmonic number 5943057120 which is 5-abundant, having an abundancy index 5.067...
%e A335318 The first 7 harmonic numbers are 1, 6, 28, 140, 270, 496 and 672. Their abundancy indices are 1, 2, 2, 2.4, 2.666..., 2 and 3. The record values, 1, 2, 2.4, 2.666... and 3 occur at 1, 6, 140, 270 and 672, the first 5 terms of this sequence.
%t A335318 rm = 0; s = {}; Do[h = DivisorSigma[0, n]/(r = DivisorSigma[1, n]/n); If[IntegerQ[h] && r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^6}]; s
%Y A335318 Cf. A000203, A001599, A335316, A335317.
%K A335318 nonn,more
%O A335318 1,2
%A A335318 _Amiram Eldar_, May 31 2020