cp's OEIS Frontend

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

%I A363944 #9 Jul 01 2023 20:54:12
%S A363944 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,
%T A363944 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,
%U A363944 5,3,19,3,6,3,20,2,21,7,3,4,5,3,22,2,2,7
%N A363944 Mean of the multiset of prime indices of n, rounded up.
%C A363944 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 A363944 Extending the terminology introduced at A124944, this is the "high mean" of prime indices.
%e A363944 The prime indices of 360 are {1,1,1,2,2,3}, with mean 3/2, so a(360) = 2.
%t A363944 prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
%t A363944 meanup[y_]:=If[Length[y]==0,0,Ceiling[Mean[y]]];
%t A363944 Table[meanup[prix[n]],{n,100}]
%Y A363944 Positions of first appearances are 1 and A000040.
%Y A363944 Positions of 1's are A000079(n>0).
%Y A363944 Before rounding up we had A326567/A326568.
%Y A363944 For mode instead of mean we have A363487, low A363486.
%Y A363944 For median instead of mean we have A363942, triangle A124944.
%Y A363944 Rounding down instead of up gives A363943, triangle A363945.
%Y A363944 The triangle for this statistic (high mean) is A363946.
%Y A363944 A112798 lists prime indices, length A001222, sum A056239.
%Y A363944 A316413 ranks partitions with integer mean, counted by A067538.
%Y A363944 A360005 gives twice the median of prime indices.
%Y A363944 A363947 ranks partitions with rounded mean 1, counted by A363948.
%Y A363944 A363949 ranks partitions with low mean 1, counted by A025065.
%Y A363944 A363950 ranks partitions with low mean 2, counted by A026905 redoubled.
%Y A363944 Cf. A051293, A124943, A215366, A327473, A327476, A327482, A359889, A362611, A363723, A363724, A363727, A363951.
%K A363944 nonn
%O A363944 1,3
%A A363944 _Gus Wiseman_, Jun 30 2023