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%I #6 Aug 05 2024 08:44:07
%S 0,1,1,2,1,1,1,3,2,1,1,2,1,1,1,4,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,5,1,1,
%T 1,3,1,1,1,3,1,1,1,2,2,1,1,4,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,6,1,1,1,2,
%U 1,1,1,4,1,1,2,2,1,1,1,4,4,1,1,2,1,1,1
%N Number of maximal strictly increasing runs in the weakly increasing prime factors of n.
%C For n > 1, this is one more than the number of adjacent equal terms in the multiset of prime factors of n.
%H Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%F For n > 1, a(n) = A046660(n) + 1 = A001222(n) - A001221(n) + 1.
%e The prime factors of 540 are {2,2,3,3,3,5}, with maximal strictly increasing runs ({2},{2,3},{3},{3,5}), so a(540) = 4.
%t Table[Length[Split[Flatten[ConstantArray@@@FactorInteger[n]],Less]],{n,100}]
%Y For compositions we have A124768, row-lengths of A374683, sum A374684.
%Y For sum of prime indices we have A374706.
%Y Row-lengths of A375128.
%Y A112798 lists prime indices:
%Y - distinct A001221
%Y - length A001222
%Y - leader A055396
%Y - sum A056239
%Y - reverse A296150
%Y Cf. A034296, A046660, A066328, A141199, A141809, A279790, A320324, A333213, A358836, A374700.
%K nonn
%O 1,4
%A _Gus Wiseman_, Aug 04 2024