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 A363234 #29 Jun 05 2023 17:29:00
%S A363234 1,2,12,720,151200,4191264000,251727315840000,1542111744113740800000,
%T A363234 10769764221549079560253440000000,
%U A363234 12109394351419848024974600399142912000000000,78344066654781231654807043124290195568885760000000000,188552692884723759943358058475004257579791386442930585600000000000
%N A363234 Least number divisible by the first n primes whose factorization into maximal prime powers, if ordered by increasing prime divisor, then has these prime power factors in decreasing order.
%C A363234 a(n) is the least number in A347284 divisible by prime(n).
%C A363234 Also a(n) is the smallest positive integer divisible by prime(n) and prime(i)^e(i) > prime(i + 1)^e(i + 1) where e(k) is the valuation of prime(k) in a(n) and 1 <= i < n. - _David A. Corneth_, May 24 2023
%C A363234 Equivalently, we can say a(n) is the least number divisible by prime(n) in A363063. This is true also of A363098, the primitive terms of A363063. {a(n)} is the intersection of A347284 and A363098. - _Peter Munn_, May 29 2023
%C A363234 If we change the end of the sequence name from "decreasing order" to "increasing order", we get the primorial numbers (A002110). - _Peter Munn_, Jun 04 2023
%H A363234 Michael De Vlieger, <a href="/A363234/a363234.png">Plot prime(i)^k | a(n) at (x,y) = (k,-n)</a> for n = 1..503.
%F A363234 a(n) = A347284(A347355(n)).
%e A363234 Table shows a(n) = A347284(j) = Product p(i)^m(i), m(i) is the i-th term read from left to right, delimited by ".", in row a(n) of A067255. Example: "4.2.1" signifies 2^4 * 3^2 * 5^1 = 720.
%e A363234 n j A067255(a(n)) a(n)
%e A363234 -------------------------------------------------------------
%e A363234 0 0 1
%e A363234 1 1 1 2
%e A363234 2 2 2.1 12
%e A363234 3 4 4.2.1 720
%e A363234 4 5 5.3.2.1 151200
%e A363234 5 8 8.5.3.2.1 4191264000
%e A363234 6 10 10.6.4.3.2.1 251727315840000
%e A363234 7 13 13.8.5.4.3.2.1 1542111744113740800000
%e A363234 8 18 18.11.7.5.4.3.2.1 10769764221549079560253440000000
%e A363234 ...
%t A363234 nn = 120; a[0] = {0}; Do[b = {2^k}; Do[If[Last[b] == 1, Break[], i = 1; p = Prime[j]; While[p^i < b[[j - 1]], i++]; AppendTo[b, p^(i - 1)]], {j, 2, k}]; Set[a[k], b], {k, nn}]; s = DeleteCases[Array[a, nn], 1, {2}]; {1}~Join~Table[Times @@ s[[FirstPosition[s, _?(Length[#] == k &)][[1]]]], {k, Max[Length /@ s]}]
%t A363234 (* Generate terms from the linked image. Caution, terms become very large. *)
%t A363234 img = Import["https://oeis.org/A363234/a363234.png", "Image"]; Map[Times @@ MapIndexed[Prime[First[#2]]^#1 &, Reverse@ #] &, SplitBy[Position[ImageData[img][[1 ;; 12]], 0.], First][[All, All, -1]] ]
%o A363234 (PARI) a(n) = {resf = matrix(n, 2); resf[,1] = primes(n)~; resf[n, 2] = 1; forstep(j = n-1, 1, -1, resf[j, 2] = logint(resf[j+1, 1]^resf[j+1, 2], resf[j, 1]) + 1); factorback(resf)} \\ _David A. Corneth_, May 24 2023
%Y A363234 Cf. A002110, A067255, A347355.
%Y A363234 Subsequence of A347284, A363063, A363098.
%K A363234 nonn,easy
%O A363234 0,2
%A A363234 _Michael De Vlieger_ and _David A. Corneth_, May 22 2023