A363944 Mean of the multiset of prime indices of n, rounded up.

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

Extending the terminology introduced at A124944, this is the "high mean" of prime indices.

Links

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

Example

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

Mathematica

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

Crossrefs

Positions of first appearances are 1 and A000040.

Positions of 1's are A000079(n>0).

Before rounding up we had A326567/A326568.

For mode instead of mean we have A363487, low A363486.

For median instead of mean we have A363942, triangle A124944.

Rounding down instead of up gives A363943, triangle A363945.

The triangle for this statistic (high mean) is A363946.

A112798 lists prime indices, length A001222, sum A056239.

A316413 ranks partitions with integer mean, counted by A067538.

A360005 gives twice the median of prime indices.

A363947 ranks partitions with rounded mean 1, counted by A363948.

A363949 ranks partitions with low mean 1, counted by A025065.

A363950 ranks partitions with low mean 2, counted by A026905 redoubled.

Cf. A051293, A124943, A215366, A327473, A327476, A327482, A359889, A362611, A363723, A363724, A363727, A363951.

Sequence in context: A318574 A277564 A363489 * A367581 A323355 A367587

Adjacent sequences: A363941 A363942 A363943 * A363945 A363946 A363947

Keyword

nonn

Author

Gus Wiseman, Jun 30 2023

Status

approved