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%I #11 Feb 16 2023 09:44:48
%S 2,3,4,5,7,8,9,10,11,13,16,17,19,20,21,22,23,25,27,29,30,31,32,34,37,
%T 39,40,41,42,43,44,46,47,49,50,53,55,57,59,60,61,62,63,64,66,67,68,70,
%U 71,73,78,79,80,81,82,83,84,85,87,88,89,90,91,92,94,97,100
%N Numbers > 1 whose distinct prime indices have integer median.
%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.
%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 900 are {1,1,2,2,3,3}, with distinct parts {1,2,3}, with median 2, so 900 is in the sequence.
%e The prime indices of 330 are {1,2,3,5}, with distinct parts {1,2,3,5}, with median 5/2, so 330 is not in the sequence.
%t Select[Range[2,100],IntegerQ[Median[PrimePi/@First/@FactorInteger[#]]]&]
%Y For mean instead of median we have A326621.
%Y Positions of even terms in A360457.
%Y The complement (without 1) is A360551.
%Y Partitions with these Heinz numbers are counted by A360686.
%Y - For divisors (A063655) we have A139711, complement A139710.
%Y - For prime indices (A360005) we have A359908, complement A359912.
%Y - For distinct prime indices (A360457) we have A360550, complement A360551.
%Y - For distinct prime factors (A360458) we have A360552, complement A100367.
%Y - For prime factors (A360459) we have A359913, complement A072978.
%Y - For prime multiplicities (A360460) we have A360553, complement A360554.
%Y - For 0-prepended differences (A360555) we have A360556, complement A360557.
%Y A112798 lists prime indices, length A001222, sum A056239.
%Y A304038 lists distinct prime indices, length A001221, sum A066328.
%Y A325347 = partitions w/ integer median, complement A307683, strict A359907.
%Y A326619/A326620 gives mean of distinct prime indices.
%Y A359893 and A359901 count partitions by median, odd-length A359902.
%Y Cf. A000975, A026424, A316413, A360006, A360009, A360248, A360453.
%K nonn
%O 1,1
%A _Gus Wiseman_, Feb 14 2023