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Numbers > 1 whose unordered prime signature has non-integer median.
13

%I #5 Feb 18 2023 15:29:11

%S 12,18,20,28,44,45,48,50,52,63,68,72,75,76,80,92,98,99,108,112,116,

%T 117,124,147,148,153,162,164,171,172,175,176,188,192,200,207,208,212,

%U 236,242,244,245,261,268,272,275,279,284,288,292,304,316,320,325,332,333

%N Numbers > 1 whose unordered prime signature has non-integer median.

%C First differs from A187039 in having 2520 and lacking 1 and 12600.

%C A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.

%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 unordered prime signature of 2520 is {3,2,1,1}, with median 3/2, so 2520 is in the sequence.

%e The unordered prime signature of 12600 is {3,2,2,1}, with median 2, so 12600 is not in the sequence.

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

%Y A subset of A030231.

%Y For mean instead of median we have A070011.

%Y Positions of odd terms in A360460.

%Y The complement is A360553 (without 1), counted by A360687.

%Y - For divisors (A063655) we have A139710, complement A139711.

%Y - For prime indices (A360005) we have A359912, complement A359908.

%Y - For distinct prime indices (A360457) we have A360551 complement A360550.

%Y - For distinct prime factors (A360458) we have A100367, complement A360552.

%Y - For prime factors (A360459) we have A072978, complement A359913.

%Y - For prime multiplicities (A360460) we have A360554, complement A360553.

%Y - For 0-prepended differences (A360555) we have A360557, complement A360556.

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

%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, A304038, A316413, A326621, A348551, A360006, A360009, A360248, A360453.

%K nonn

%O 1,1

%A _Gus Wiseman_, Feb 16 2023