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Numbers > 1 whose distinct prime factors have integer median.
10

%I #5 Feb 16 2023 13:41:53

%S 2,3,4,5,7,8,9,11,13,15,16,17,19,21,23,25,27,29,30,31,32,33,35,37,39,

%T 41,42,43,45,47,49,51,53,55,57,59,60,61,63,64,65,66,67,69,70,71,73,75,

%U 77,78,79,81,83,84,85,87,89,90,91,93,95,97,99,101,102,103

%N Numbers > 1 whose distinct prime factors have integer median.

%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 factors of 900 are {2,2,3,3,5,5}, with distinct parts {2,3,5}, with median 3, so 900 is in the sequence.

%t Select[Range[2,100],IntegerQ[Median[First/@FactorInteger[#]]]&]

%Y For mean instead of median we have A078174, complement of A176587.

%Y The complement is A100367 (without 1).

%Y Positions of even terms in A360458.

%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 A027746 lists prime factors, length A001222, indices A112798.

%Y A027748 lists distinct prime factors, length A001221, indices A304038.

%Y A323171/A323172 = mean of distinct prime factors, indices A326619/A326620.

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

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

%Y Cf. A000975, A026424, A056239, A078175, A175352, A316413, A326621, A360009.

%K nonn

%O 1,1

%A _Gus Wiseman_, Feb 16 2023