A360005 Two times the median of the multiset of prime indices of n.

2, 4, 2, 6, 3, 8, 2, 4, 4, 10, 2, 12, 5, 5, 2, 14, 4, 16, 2, 6, 6, 18, 2, 6, 7, 4, 2, 20, 4, 22, 2, 7, 8, 7, 3, 24, 9, 8, 2, 26, 4, 28, 2, 4, 10, 30, 2, 8, 6, 9, 2, 32, 4, 8, 2, 10, 11, 34, 3, 36, 12, 4, 2, 9, 4, 38, 2, 11, 6, 40, 2, 42, 13, 6, 2, 9, 4, 44, 2

Offset: 2

Author

Gus Wiseman, Jan 23 2023

Keywords

• nonn

Comments

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.

The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Examples

			The prime indices of 360 are {1,1,1,2,2,3}, with median 3/2, so a(360) = 3.
		

Crossrefs

The triangle for this statistic is A359893, cf. A359901, A359902.

Positions of even terms are A359908, odd A359912.

Positions of first appearances are A360006, sorted A360007.

A112798 lists prime indices, length A001222, sum A056239.

A316413 lists numbers whose prime indices have integer mean.

A325347 = partitions w/ integer median, strict A359907, complement A307683.

A326567/A326568 gives mean of prime indices.

Cf. A026424, A359889, A359890, A360009.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[2*Median[prix[n]],{n,2,100}]