%I #5 Aug 30 2022 09:41:31
%S 2,3,4,5,6,7,8,9,2,5,11,12,13,2,7,15,16,17,18,19,4,5,3,7,2,11,23,24,
%T 25,2,13,27,4,7,29,30,31,32,3,11,2,17,35,36,37,2,19,3,13,8,5,41,6,7,
%U 43,4,11,45,2,23,47,48,49,2,25,3,17,4,13,53,54,5,11,8
%N Irregular triangle read by rows where row n is the ordered factorization of n into maximal gapless divisors.
%C Row-products are the positive integers 1, 2, 3, ...
%e The first 16 rows:
%e 1 =
%e 2 = 2
%e 3 = 3
%e 4 = 4
%e 5 = 5
%e 6 = 6
%e 7 = 7
%e 8 = 8
%e 9 = 9
%e 10 = 2 * 5
%e 11 = 11
%e 12 = 12
%e 13 = 13
%e 14 = 2 * 7
%e 15 = 15
%e 16 = 16
%e The factorization of 18564 is 18564 = 12*7*221, so row 18564 is {12,7,221}.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Times@@Prime/@#&/@Split[primeMS[n],#1>=#2-1&],{n,100}]
%Y Row-lengths are A287170, firsts A066205, even bisection A356229.
%Y Applying bigomega to all parts gives A356226, statistics A356227-A356232.
%Y A001055 counts factorizations.
%Y A001221 counts distinct prime factors, sum A001414.
%Y A003963 multiplies together the prime indices.
%Y A056239 adds up the prime indices, row sums of A112798.
%Y A132747 counts non-isolated divisors, complement A132881.
%Y A356069 counts gapless divisors, initial A356224 (complement A356225).
%Y Cf. A000005, A001222, A060680-A060683, A073491-A073495, A193829, A330103, A356233-A356237.
%K nonn,tabf
%O 1,1
%A _Gus Wiseman_, Aug 28 2022