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

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

Offset: 1

Author

Gus Wiseman, Jul 01 2023

Keywords

• nonn

Comments

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).

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.

Examples

			The prime indices of 90 are {1,2,2,3}, with high median 2, so a(90) = 2.
The prime indices of 150 are {1,2,3,3}, with high median 3, so a(150) = 3.
		

Crossrefs

Positions of first appearances are 1 and A000040.

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

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

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

The low version is A363941.

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

A061395 give maximum prime index, A055396 minimum.

A112798 lists prime indices, length A001222, sum A056239.

A362611 counts modes in prime indices, triangle A362614.

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

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
merr[y_]:=If[Length[y]==0,0, If[OddQ[Length[y]],y[[(Length[y]+1)/2]],y[[1+Length[y]/2]]]];
Table[merr[prix[n]],{n,100}]