%I #9 Jul 02 2023 09:02:13

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

%T 7,4,2,12,8,6,1,13,2,14,1,2,9,15,1,4,3,7,1,16,2,5,1,8,10,17,2,18,11,2,

%U 1,6,2,19,1,9,3,20,1,21,12,3,1,5,2,22,1,2

%N High median in the multiset of prime indices of n.

%C The high median (see A124944) in a multiset is either the middle part (for odd length), or the greatest of the two middle parts (for even length).

%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.

%e The prime indices of 90 are {1,2,2,3}, with high median 2, so a(90) = 2.

%e The prime indices of 150 are {1,2,3,3}, with high median 3, so a(150) = 3.

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

%t merr[y_]:=If[Length[y]==0,0, If[OddQ[Length[y]],y[[(Length[y]+1)/2]],y[[1+Length[y]/2]]]];

%t Table[merr[prix[n]],{n,100}]

%Y Positions of first appearances are 1 and A000040.

%Y The triangle for this statistic (high median) is A124944, low A124943.

%Y Regular median of prime indices is A360005(n)/2.

%Y For mode instead of median we have A363487, low A363486.

%Y The low version is A363941.

%Y For mean instead of median we have A363944, triangle A363946, low A363943.

%Y A061395 give maximum prime index, A055396 minimum.

%Y A112798 lists prime indices, length A001222, sum A056239.

%Y A362611 counts modes in prime indices, triangle A362614.

%Y Cf. A025065, A215366, A316413, A326567/A326568, A359889, A359908, A359912, A363727, A363949, A363950.

%K nonn

%O 1,3

%A _Gus Wiseman_, Jul 01 2023