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 A307322 #9 Apr 19 2019 13:48:59
%S A307322 0,1,1,1,2,1,2,1,1,2,2,2,1,1,1,2,1,3,1,1,3,2,3,1,1,1,3,1,2,3,1,1,2,3,
%T A307322 1,1,4,2,4,1,1,1,4,1,2,4,1,1,2,4,1,1,1,2,4,1,2,2,4,1,1,3,4,1,2,5,1,1,
%U A307322 2,5,1,1,1,2,5,1,2,2,5,1,1,3,5,1,1,2,2
%N A307322 Irregular triangle where row n is a list of indices in A002110 with multiplicity whose product is A004394(n).
%C A307322 Analogous to A306737.
%C A307322 The first 52 terms of a(n) and A306737 are identical, since the first 19 terms of A002182 and A004394 are the same, and the first two terms of row 20 are the same. a(20) = 4,2,1,1,1, while A306737(20) = 4,2,2.
%C A307322 Each superabundant number A004394(n) can be expressed as a product of primorials in A002110.
%C A307322 Row 1 = {0} by convention.
%C A307322 Maximum value in row n = A001221(A004394(n)).
%C A307322 Row n in reverse order is the conjugate of the list of the multiplicities of the prime divisors of A004394(n).
%H A307322 Michael De Vlieger, <a href="/A307322/b307322.txt">Table of n, a(n) for n = 1..10664</a> (rows 1 <= n <= 1200, flattened).
%H A307322 Michael De Vlieger, <a href="/A307322/a307322.txt">Relation between A307322 and A306737</a>.
%e A307322 Terms in the first rows n of this sequence, followed by the corresponding primorials whose product = A004394(n):
%e A307322 n T(n,k) A002110(T(n,k)) A004394(n)
%e A307322 -----------------------------------------------
%e A307322 1: 0; 1 = 1
%e A307322 2: 1; 2 = 2
%e A307322 3: 1, 1; 2 * 2 = 4
%e A307322 4: 2; 6 = 6
%e A307322 5: 1, 2; 2 * 6 = 12
%e A307322 6: 1, 1, 2; 2 * 2 * 6 = 24
%e A307322 7: 2, 2; 6 * 6 = 36
%e A307322 8: 1, 1, 1, 2; 2 * 2 * 2 * 6 = 48
%e A307322 9: 1, 3; 2 * 30 = 60
%e A307322 10: 1, 1, 3; 2 * 2 * 30 = 120
%e A307322 11: 2, 3; 6 * 30 = 180
%e A307322 12: 1, 1, 1, 3; 2 * 2 * 2 * 30 = 240
%e A307322 13: 1, 2, 3; 2 * 6 * 30 = 360
%e A307322 14: 1, 1, 2, 3; 2 * 2 * 6 * 30 = 720
%e A307322 15: 1, 1, 4; 2 * 2 * 210 = 840
%e A307322 ...
%e A307322 Row 6 = {1,1,2} since A002110(1)*A002110(1)*A002110(2) = 2*2*6 = 24 and A004394(6) = 24. The conjugate of {1,1,2} = {3,1} and 24 = 2^3 * 3^1.
%e A307322 Row 10 = {1,1,3} since A002110(1)*A002110(1)*A002110(3) = 2*2*30 = 120 and A004394(10) = 120. The conjugate of {1,1,3} = {3,1,1} and 120 = 2^3 * 3^1 * 5^1.
%t A307322 Block[{s = Array[DivisorSigma[1, #]/# &, 10^6]}, Map[Table[LengthWhile[#, # >= i &], {i, Max@ #}] &@ If[# == 1, {0}, Function[f, ReplacePart[Table[0, {PrimePi[f[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, f]]@ FactorInteger@ #] &@ FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] /. {} -> {0}] // Flatten
%Y A307322 Cf. A001221, A002110, A002182, A004394, A306737.
%K A307322 nonn,tabf
%O A307322 1,5
%A A307322 _Michael De Vlieger_, Apr 02 2019