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

2,1

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).

Links

Table of n, a(n) for n=2..80.

Example

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

Mathematica

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

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.

Sequence in context: A105393 A182812 A354266 * A360457 A328985 A328196

Adjacent sequences: A360002 A360003 A360004 * A360006 A360007 A360008

Keyword

nonn

Author

Gus Wiseman, Jan 23 2023

Status

approved