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 A347354 #10 Sep 25 2021 14:59:25
%S A347354 1,2,1,3,4,1,2,5,1,6,1,2,7,1,3,2,1,8,1,4,2,1,9,10,1,2,11,1,3,1,2,12,1,
%T A347354 4,13,1,2,1,14,15,1,2,3,1,6,2,1,4,1,16,2,1,17,18,1,2,1,3,5,1,2,19,1,4,
%U A347354 2,1,20,1,3,21,1,2,22,1,9,1,2,4,1,8,2,1,3
%N A347354 a(n) = sum of T(n,k) - T(n-1,k) for row n of A347285.
%C A347354 If for row n, k > A089576(n-1), we interpret T(n-1,k) = 0.
%C A347354 Also the length of d = T(n,k) - T(n-1,k) in row n of A347285 such that d > 1, with 0 <= d <= 1.
%C A347354 Compactification of A347284 via indices k of primorials A002110(k). This is the most efficient compactification of A347284, superior to binary compactification via A347287. It employs the fact that A347284 concerns products of primorials, i.e., is a subset of A025487.
%C A347354 We can construct row n of A347285 by summing a constant array of a(k) 1's for 1 <= k <= n-1.
%H A347354 Michael De Vlieger, <a href="/A347354/b347354.txt">Table of n, a(n) for n = 1..10000</a>
%F A347354 A347284(n) = Product_{k=1..n} A002110(a(k)).
%e A347354 Relation of a(n) and irregular triangle A347285, placing "." after the term in the current row where T(n,k) no longer exceeds T(n-1,k). Since the rows of A347285 reach a fixed point of 0, we interpret T(n,k) for vacant T(n-1,k) as exceeding same.
%e A347354 n Row n of A347285 a(n)
%e A347354 -----------------------------
%e A347354 0: 0
%e A347354 1: 1. 1
%e A347354 2: 2 1. 2
%e A347354 3: 3. 1 1
%e A347354 4: 4 2 1. 3
%e A347354 5: 5 3 2 1. 4
%e A347354 6: 6. 3 2 1 1
%e A347354 7: 7 4. 2 1 2
%e A347354 8: 8 5 3 2 1. 5
%e A347354 9: 9. 5 3 2 1 1
%e A347354 10: 10 6 4 3 2 1. 6
%e A347354 ...
%e A347354 a(3) = 1 since row 3 of A347285 has {3,1} while row 2 has {2,1}; only the first term of the former exceeds the analogous term in the latter.
%e A347354 a(4) = 3 since row 4 = {4,2,1} and row 3 = {3,1}; all 3 terms of the former are larger than the analogous term in the latter, etc.
%t A347354 Block[{nn = 84, a = {0}, c, e, m}, e[1] = 0; Do[c = 1; e[1]++; Do[Set[m, j]; Which[e[j - 1] == 1, Break[], IntegerQ@ e[j], If[e[j] < #, e[j]++; c++] &@ Floor@ Log[Prime[j], Prime[j - 1]^e[j - 1]], True, Set[e[j], 1]], {j, 2, k}]; AppendTo[a, c + Boole[c == m - 2]], {k, 2, nn}]; MapAt[# - 1 &, a, 4]]
%Y A347354 Cf. A002110, A025487, A089576, A347284, A347285, A347287.
%K A347354 nonn
%O A347354 1,2
%A A347354 _Michael De Vlieger_, Sep 16 2021