cp's OEIS Frontend

A363942 High median in the multiset of prime indices of n.

%I A363942 #9 Jul 02 2023 09:02:13
%S A363942 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 A363942 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 A363942 1,6,2,19,1,9,3,20,1,21,12,3,1,5,2,22,1,2
%N A363942 High median in the multiset of prime indices of n.
%C A363942 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 A363942 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 A363942 The prime indices of 90 are {1,2,2,3}, with high median 2, so a(90) = 2.
%e A363942 The prime indices of 150 are {1,2,3,3}, with high median 3, so a(150) = 3.
%t A363942 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363942 merr[y_]:=If[Length[y]==0,0, If[OddQ[Length[y]],y[[(Length[y]+1)/2]],y[[1+Length[y]/2]]]];
%t A363942 Table[merr[prix[n]],{n,100}]
%Y A363942 Positions of first appearances are 1 and A000040.
%Y A363942 The triangle for this statistic (high median) is A124944, low A124943.
%Y A363942 Regular median of prime indices is A360005(n)/2.
%Y A363942 For mode instead of median we have A363487, low A363486.
%Y A363942 The low version is A363941.
%Y A363942 For mean instead of median we have A363944, triangle A363946, low A363943.
%Y A363942 A061395 give maximum prime index, A055396 minimum.
%Y A363942 A112798 lists prime indices, length A001222, sum A056239.
%Y A363942 A362611 counts modes in prime indices, triangle A362614.
%Y A363942 Cf. A025065, A215366, A316413, A326567/A326568, A359889, A359908, A359912, A363727, A363949, A363950.
%K A363942 nonn
%O A363942 1,3
%A A363942 _Gus Wiseman_, Jul 01 2023