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 A356226 #11 Aug 13 2022 22:24:56
%S A356226 1,1,2,1,2,1,3,2,1,1,1,3,1,1,1,2,4,1,3,1,2,1,1,1,1,1,1,4,2,1,1,3,2,1,
%T A356226 1,3,1,5,1,1,1,1,2,4,1,1,1,1,1,3,1,1,2,1,1,2,1,3,1,1,1,5,2,1,2,1,1,2,
%U A356226 1,1,4,1,1,3,1,1,1,1,1,1,4,1,1,1,2,1,6
%N A356226 Irregular triangle giving the lengths of maximal gapless submultisets of the prime indices of n.
%C A356226 A sequence is gapless if it covers an unbroken interval of positive integers. For example, the multiset {2,3,5,5,6,9} has three maximal gapless submultisets: {2,3}, {5,5,6}, {9}.
%C A356226 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A356226 Triangle begins: {}, {1}, {1}, {2}, {1}, {2}, {1}, {3}, {2}, {1,1}, {1}, {3}, {1}, {1,1}, {2}, {4}, {1}, {3}, {1}, {2,1}, ... For example, the prime indices of 20 are {1,1,3}, which separates into maximal gapless submultisets {{1,1},{3}}, so row 20 is (2,1).
%e A356226 The prime indices of 18564 are {1,1,2,4,6,7}, which separates into {1,1,2}, {4}, {6,7}, so row 18564 is (3,1,2). This corresponds to the factorization 18564 = 12 * 7 * 221.
%t A356226 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A356226 Table[Length/@Split[primeMS[n],#1>=#2-1&],{n,100}]
%Y A356226 Row sums are A001222.
%Y A356226 Singleton row positions are A073491, complement A073492.
%Y A356226 Length-2,3,4 row positions are A073493-A073495.
%Y A356226 Row lengths are A287170, firsts A066205.
%Y A356226 Row minima are A356227.
%Y A356226 Row maxima are A356228.
%Y A356226 Bisected run-lengths are A356229.
%Y A356226 Standard composition numbers of rows are A356230.
%Y A356226 Heinz numbers of rows are A356231.
%Y A356226 Positions of first appearances are A356232.
%Y A356226 A001221 counts distinct prime factors, with sum A001414.
%Y A356226 A001223 lists the prime gaps, reduced A028334.
%Y A356226 A003963 multiplies together the prime indices of n.
%Y A356226 A056239 adds up prime indices, row sums of A112798.
%Y A356226 A132747 counts non-isolated divisors, complement A132881.
%Y A356226 A356069 counts gapless divisors, initial A356224 (complement A356225).
%Y A356226 Cf. A000005, A055874, A060680-A060683, A137921, A193829, A286470, A328166.
%K A356226 nonn,tabf
%O A356226 1,3
%A A356226 _Gus Wiseman_, Aug 10 2022