A360005 - OEIS

%I #6 Jan 23 2023 12:41:26

%S 2,4,2,6,3,8,2,4,4,10,2,12,5,5,2,14,4,16,2,6,6,18,2,6,7,4,2,20,4,22,2,

%T 7,8,7,3,24,9,8,2,26,4,28,2,4,10,30,2,8,6,9,2,32,4,8,2,10,11,34,3,36,

%U 12,4,2,9,4,38,2,11,6,40,2,42,13,6,2,9,4,44,2

%N Two times the median of the multiset of prime indices of n.

%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 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

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

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Table[2*Median[prix[n]],{n,2,100}]

%Y The triangle for this statistic is A359893, cf. A359901, A359902.

%Y Positions of even terms are A359908, odd A359912.

%Y Positions of first appearances are A360006, sorted A360007.

%Y A112798 lists prime indices, length A001222, sum A056239.

%Y A316413 lists numbers whose prime indices have integer mean.

%Y A325347 = partitions w/ integer median, strict A359907, complement A307683.

%Y A326567/A326568 gives mean of prime indices.

%Y Cf. A026424, A359889, A359890, A360009.

%K nonn

%O 2,1

%A _Gus Wiseman_, Jan 23 2023