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 A365902 #13 Jan 20 2024 09:23:00
%S A365902 1,2,6,4,12,60,24,120,840,36,180,1260,48,240,1680,360,2520,27720,720,
%T A365902 5040,55440,720720,7560,83160,1081080,10080,110880,1441440,15120,
%U A365902 166320,2162160,36756720,698377680,20160,221760,2882880,25200,277200,3603600,61261200,332640
%N A365902 Irregular triangle of highly composite numbers h(n) = A002182(n) arranged first according to rad(h(n))/h(n) then by rad(h(n)), where rad(n) = A007947(n).
%C A365902 rad(h(n)) = P(omega(h(n))), where P(n) = A002110(n) and omega(n) = A001221(n).
%C A365902 This sequence merely lists terms in row n, it does not reflect S(n,j) = A301414(n)*P(j), where P(j) = rad(A301414(n)*P(j)), since least j > 0 for n > 1.
%H A365902 Michael De Vlieger, <a href="/A365902/b365902.txt">Table of n, a(n) for n = 1..10598</a> (rows n = 1..640, flattened)
%H A365902 Michael De Vlieger, <a href="/A365902/a365902_1.png">Logarithmic scatterplot of log_10 a(n)</a>, n = 1..10^4.
%H A365902 Michael De Vlieger, <a href="/A365902/a365902.png">Image showing 8000 rows of this sequence</a> (715118 HCNs), representing each term with a black pixel, extracted from the Flammenkamp dataset of 779674 HCNs. Note, the HCNs shown are not the smallest; some HCNs are clipped away from the bottom of this image where uncertainty in the completion of rows is expected.
%F A365902 Let i = least j such that A301414(n)*A002110(j) is in A002182.
%F A365902 This sequence is T(n,k) = S(n,j-i+1).
%F A365902 Length of row n = A301415(n).
%e A365902 Row 1 contains the products of A301414(1) = 1 and each of P(0) = 1, P(1) = 2, and P(2) = 6.
%e A365902 Row 2 contains the products of A301414(2) = 2 and each of P(1), P(2), and P(3) = 30.
%e A365902 Row 3 contains the products of A301414(3) = 4 and each of P(2) and P(3), etc.
%e A365902 Table of first rows of S(n,j), where for S(n,j) = A002182(i), j = A108602(i):
%e A365902 n\j | 0 1 2 3 4 5
%e A365902 ----------------------------------
%e A365902 1 | 1, 2, 6
%e A365902 2 | 4, 12, 60
%e A365902 3 | 24, 120
%e A365902 4 | 36, 180, 1260
%e A365902 5 | 48, 240, 1680
%e A365902 6 | 360, 2520, 27720
%e A365902 7 | 720, 5040, 720720, etc.
%e A365902 In this sequence T(n,k) we have the following:
%e A365902 1: 1, 2, 6;
%e A365902 2: 4, 12, 60;
%e A365902 3: 24, 120;
%e A365902 4: 36, 180, 1260;
%e A365902 5: 48, 240, 1680;
%e A365902 6: 360, 2520, 27720;
%e A365902 7: 720, 5040, 720720; etc.
%t A365902 nn = 8; rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
%t A365902 MapIndexed[Set[P[First[#2]], #1] &, FoldList[Times, Prime@ Range[nn + 1]]];
%t A365902 a2182 = Import["https://oeis.org/A002182/b002182.txt", "Data"][[All, -1]];
%t A365902 TakeWhile[
%t A365902 SplitBy[SortBy[
%t A365902 Map[{#1/#2, PrimeNu[#2], #1} & @@ {#, rad[#]} &,
%t A365902 TakeWhile[a2182, rad[#] <= P[nn] &]], #[[1 ;; 2]] &,
%t A365902 LexicographicOrder], First],
%t A365902 FreeQ[a2182, #1 P[#2 + 1]] & @@ #[[-1, 1 ;; 2]] &][[All, All, -1]] // Flatten
%Y A365902 Cf. A001221, A002110, A002182, A007947, A108602, A301414, A301415.
%K A365902 nonn,tabf
%O A365902 1,2
%A A365902 _Michael De Vlieger_, Oct 12 2023