cp's OEIS Frontend

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

%I A363943 #11 Jul 01 2023 20:54:07
%S A363943 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 A363943 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 A363943 4,2,19,3,5,2,20,1,21,6,2,3,4,3,22,1,2,7
%N A363943 Mean of the multiset of prime indices of n, rounded down.
%C A363943 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 A363943 Extending the terminology introduced at A124943, this is the "low mean" of prime indices.
%e A363943 The prime indices of 360 are {1,1,1,2,2,3}, with mean 3/2, so a(360) = 1.
%t A363943 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363943 meandown[y_]:=If[Length[y]==0,0,Floor[Mean[y]]];
%t A363943 Table[meandown[prix[n]],{n,100}]
%Y A363943 Positions of first appearances are 1 and A000040.
%Y A363943 Before rounding down we had A326567/A326568.
%Y A363943 For mode instead of mean we have A363486, high A363487.
%Y A363943 For low median instead of mean we have A363941, triangle A124943.
%Y A363943 For high median instead of mean we have A363942, triangle A124944.
%Y A363943 The high version is A363944, triangle A363946.
%Y A363943 The triangle for this statistic (low mean) is A363945.
%Y A363943 Positions of 1's are A363949(n) = 2*A344296(n), counted by A025065.
%Y A363943 A088529/A088530 gives mean of prime signature A124010.
%Y A363943 A112798 lists prime indices, length A001222, sum A056239.
%Y A363943 A316413 ranks partitions with integer mean, counted by A067538.
%Y A363943 A360005 gives twice the median of prime indices.
%Y A363943 A363947 ranks partitions with rounded mean 1, counted by A363948.
%Y A363943 Cf. A102627, A327473, A327476, A327482, A348551, A359889, A363727, A363951.
%K A363943 nonn
%O A363943 1,3
%A A363943 _Gus Wiseman_, Jun 29 2023