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 A375136 #6 Aug 05 2024 08:44:07
%S A375136 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 A375136 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 A375136 1,1,1,4,1,1,2,2,1,1,1,4,4,1,1,2,1,1,1
%N A375136 Number of maximal strictly increasing runs in the weakly increasing prime factors of n.
%C A375136 For n > 1, this is one more than the number of adjacent equal terms in the multiset of prime factors of n.
%H A375136 Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%F A375136 For n > 1, a(n) = A046660(n) + 1 = A001222(n) - A001221(n) + 1.
%e A375136 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 A375136 Table[Length[Split[Flatten[ConstantArray@@@FactorInteger[n]],Less]],{n,100}]
%Y A375136 For compositions we have A124768, row-lengths of A374683, sum A374684.
%Y A375136 For sum of prime indices we have A374706.
%Y A375136 Row-lengths of A375128.
%Y A375136 A112798 lists prime indices:
%Y A375136 - distinct A001221
%Y A375136 - length A001222
%Y A375136 - leader A055396
%Y A375136 - sum A056239
%Y A375136 - reverse A296150
%Y A375136 Cf. A034296, A046660, A066328, A141199, A141809, A279790, A320324, A333213, A358836, A374700.
%K A375136 nonn
%O A375136 1,4
%A A375136 _Gus Wiseman_, Aug 04 2024