A374706 - OEIS

%I #6 Aug 05 2024 08:44:30

%S 0,1,2,2,3,1,4,3,4,1,5,2,6,1,2,4,7,3,8,2,2,1,9,3,6,1,6,2,10,1,11,5,2,

%T 1,3,4,12,1,2,3,13,1,14,2,4,1,15,4,8,4,2,2,16,5,3,3,2,1,17,2,18,1,4,6,

%U 3,1,19,2,2,1,20,5,21,1,5,2,4,1,22,4,8,1

%N Sum of minima of the maximal strictly increasing runs in the weakly increasing prime indices of n.

%C 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.

%H Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.

%e The prime indices of 540 are {1,1,2,2,2,3}, with strictly increasing runs ({1},{1,2},{2},{2,3}), with minima (1,1,2,2), summing to a(540) = 6.

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Table[Total[First/@Split[prix[n],Less]],{n,100}]

%Y For leaders of constant runs we have A066328.

%Y A version for compositions is A374684, row-sums of A374683 (length A124768).

%Y Row-sums of A375128.

%Y For length instead of sum we have A375136.

%Y A055887 counts sequences of partitions with total sum n.

%Y A112798 lists prime indices:

%Y - length A001222, distinct A001221

%Y - leader A055396

%Y - sum A056239

%Y - reverse A296150

%Y Cf. A034296, A141199, A189076, A218482, A279790, A333213, A358836, A374634, A374700, A374758, A375133.

%K nonn

%O 1,3

%A _Gus Wiseman_, Aug 04 2024