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 A346016 #10 Nov 24 2024 11:52:12
%S A346016 1,2,4,6,12,24,30,60,120,180,210,420,840,1260,2310,4620,9240,13860,
%T A346016 27720,30030,60060,120120,180180,360360,510510,1021020,2042040,
%U A346016 3063060,6126120,9699690,19399380,38798760,58198140,116396280,223092870,446185740,892371480,1338557220
%N A346016 Numbers k where the average number of distinct prime factors of the divisors of k sets a new record.
%C A346016 First differs from A282472 at n = 48.
%C A346016 The corresponding record values are 0, 1/2, 2/3, 1, 7/6, 5/4, 3/2, 5/3, 7/4, 11/6, 2, ...
%C A346016 All the terms are least integers of their prime signature (A025487) since f(n) = A346009(n)/A346010(n) depends only on the prime signature of n.
%C A346016 This sequence is infinite since f(n) is unbounded. E.g., f(A002110(n)) = n/2.
%H A346016 Amiram Eldar, <a href="/A346016/b346016.txt">Table of n, a(n) for n = 1..198</a>
%t A346016 lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; f[p_, e_] := e/(e + 1); f[1] = 0; f[n_] := Plus @@ f @@@ FactorInteger[n]; s = {}; fmax = -1; Do[f1 = f[lps[[k]]]; If[f1 > fmax, fmax = f1; AppendTo[s, lps[[k]]]], {k, 1, Length[lps]}]; s
%t A346016 DeleteDuplicates[Table[{n,Mean[PrimeNu[Divisors[n]]]},{n,100000}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* The program generates the first 21 terms of the sequence. *) (* _Harvey P. Dale_, Nov 24 2024 *)
%Y A346016 Cf. A002110, A282472, A346009, A346010.
%Y A346016 Subsequence of A025487.
%K A346016 nonn
%O A346016 1,2
%A A346016 _Amiram Eldar_, Jul 01 2021