A363941 Low median in the multiset of prime indices of n.

0, 1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 1, 6, 1, 2, 1, 7, 2, 8, 1, 2, 1, 9, 1, 3, 1, 2, 1, 10, 2, 11, 1, 2, 1, 3, 1, 12, 1, 2, 1, 13, 2, 14, 1, 2, 1, 15, 1, 4, 3, 2, 1, 16, 2, 3, 1, 2, 1, 17, 1, 18, 1, 2, 1, 3, 2, 19, 1, 2, 3, 20, 1, 21, 1, 3, 1, 4, 2, 22, 1, 2, 1

Offset: 1

Author

Gus Wiseman, Jul 01 2023

Keywords

• nonn

Comments

The low median (see A124943) in a multiset is either the middle part (for odd length), or the least 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 low median 2, so a(90) = 2.
The prime indices of 150 are {1,2,3,3}, with low median 2, so a(150) = 2.
		

Crossrefs

Positions of first appearances are 1 and A000040.

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

Median of prime indices is A360005(n)/2.

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

Positions of 1's are A363488.

The high version is A363942.

A067538 counts partitions with integer mean, ranked by A316413.

A112798 lists prime indices, length A001222, sum A056239.

A363943 gives low mean of prime indices, triangle A363945.

A363944 gives high mean of prime indices, triangle A363946.

Cf. A025065, A215366, A326567/A326568, A344296, A359889, A359908, A363727, A363740.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
mell[y_]:=If[Length[y]==0,0, If[OddQ[Length[y]],y[[(Length[y]+1)/2]],y[[Length[y]/2]]]];
Table[mell[prix[n]],{n,30}]