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

1,3

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.

Links

Table of n, a(n) for n=1..81.

Example

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.

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}]

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.

Sequence in context: A367581 A323355 A367587 * A363487 A108230 A334202

Adjacent sequences: A363939 A363940 A363941 * A363943 A363944 A363945

Keyword

nonn

Author

Gus Wiseman, Jul 01 2023

Status

approved