A363943 Mean of the multiset of prime indices of n, rounded down.

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

Offset: 1

Author

Gus Wiseman, Jun 29 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.

Extending the terminology introduced at A124943, this is the "low mean" of prime indices.

Examples

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

Crossrefs

Positions of first appearances are 1 and A000040.

Before rounding down we had A326567/A326568.

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

For low median instead of mean we have A363941, triangle A124943.

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

The high version is A363944, triangle A363946.

The triangle for this statistic (low mean) is A363945.

Positions of 1's are A363949(n) = 2*A344296(n), counted by A025065.

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.

A360005 gives twice the median of prime indices.

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

Cf. A102627, A327473, A327476, A327482, A348551, A359889, A363727, A363951.

Programs

Mathematica

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