%I #6 Feb 15 2023 21:48:23

%S 1,2,4,2,6,3,8,2,4,4,10,3,12,5,5,2,14,3,16,4,6,6,18,3,6,7,4,5,20,4,22,

%T 2,7,8,7,3,24,9,8,4,26,4,28,6,5,10,30,3,8,4,9,7,32,3,8,5,10,11,34,4,

%U 36,12,6,2,9,4,38,8,11,6,40,3,42,13,5,9,9,4,44,4

%N Two times the median of the set of distinct prime indices of n; a(1) = 1.

%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). Since the denominator is always 1 or 2, the median can be represented as an integer by multiplying by 2.

%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. Distinct prime indices are listed by A304038.

%e The prime indices of 65 are {3,6}, with distinct parts {3,6}, with median 9/2, so a(65) = 9.

%e The prime indices of 900 are {1,1,2,2,3,3}, with distinct parts {1,2,3}, with median 2, so a(900) = 4.

%t Table[If[n==1,1,2*Median[PrimePi/@First/@FactorInteger[n]]],{n,100}]

%Y The version for divisors is A063655.

%Y For mean instead of two times median we have A326619/A326620.

%Y The version for all prime indices is A360005.

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

%Y The version for distinct prime factors is A360458.

%Y The version for all prime factors is A360459.

%Y The version for prime multiplicities is A360460.

%Y Positions of even terms are A360550.

%Y Positions of odd terms are A360551.

%Y The version for 0-prepended differences is A360555.

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

%Y A304038 lists distinct prime indices.

%Y A325347 counts partitions with integer median, complement A307683.

%Y A326567/A326568 gives mean of prime indices.

%Y A359893 and A359901 count partitions by median, odd-length A359902.

%Y Cf. A000975, A026424, A316413, A359907, A359908, A359912, A360248, A360453.

%K nonn

%O 1,2

%A _Gus Wiseman_, Feb 14 2023