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%I #11 Jul 01 2023 20:54:07
%S 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,
%T 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,
%U 4,2,19,3,5,2,20,1,21,6,2,3,4,3,22,1,2,7
%N Mean of the multiset of prime indices of n, rounded down.
%C 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.
%C Extending the terminology introduced at A124943, this is the "low mean" of prime indices.
%e The prime indices of 360 are {1,1,1,2,2,3}, with mean 3/2, so a(360) = 1.
%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t meandown[y_]:=If[Length[y]==0,0,Floor[Mean[y]]];
%t Table[meandown[prix[n]],{n,100}]
%Y Positions of first appearances are 1 and A000040.
%Y Before rounding down we had A326567/A326568.
%Y For mode instead of mean we have A363486, high A363487.
%Y For low median instead of mean we have A363941, triangle A124943.
%Y For high median instead of mean we have A363942, triangle A124944.
%Y The high version is A363944, triangle A363946.
%Y The triangle for this statistic (low mean) is A363945.
%Y Positions of 1's are A363949(n) = 2*A344296(n), counted by A025065.
%Y A088529/A088530 gives mean of prime signature A124010.
%Y A112798 lists prime indices, length A001222, sum A056239.
%Y A316413 ranks partitions with integer mean, counted by A067538.
%Y A360005 gives twice the median of prime indices.
%Y A363947 ranks partitions with rounded mean 1, counted by A363948.
%Y Cf. A102627, A327473, A327476, A327482, A348551, A359889, A363727, A363951.
%K nonn
%O 1,3
%A _Gus Wiseman_, Jun 29 2023
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