A363489 Rounded mean of the multiset of prime indices of n.

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

Offset

1,3

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.

We use the "rounding half to even" rule, see link.

Links

Table of n, a(n) for n=1..82.

Wikipedia, Rounding.

Example

The prime indices of 180 are {1,1,2,2,3}, with mean 9/5, which rounds to 2, so a(180) = 2.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 0, Round[Mean[prix[n]]]], {n, 100}]

Crossrefs

Positions of first appearances are 1 and A000040.

Before rounding we had A326567/A326568.

For rounded-down: A363943, triangle A363945.

For rounded-up: A363944, triangle A363946.

Positions of 1's are A363948, complement A364059.

The triangle for this statistic (rounded mean) is A364060.

For prime factors instead of indices we have A364061.

A088529/A088530 gives mean of prime signature A124010.

A112798 lists prime indices, length A001222, sum A056239.

A316413 ranks partitions with integer mean, counted by A067538.

Cf. A327473, A327476, A327482, A359889, A360005, A363947, A363949, A363951.

Sequence in context: A035491 A318574 A277564 * A363944 A367581 A323355

Adjacent sequences: A363486 A363487 A363488 * A363490 A363491 A363492

Keyword

nonn

Author

Gus Wiseman, Jul 07 2023

Status

approved