cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A360554 Numbers > 1 whose unordered prime signature has non-integer median.

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%I A360554 #5 Feb 18 2023 15:29:11
%S A360554 12,18,20,28,44,45,48,50,52,63,68,72,75,76,80,92,98,99,108,112,116,
%T A360554 117,124,147,148,153,162,164,171,172,175,176,188,192,200,207,208,212,
%U A360554 236,242,244,245,261,268,272,275,279,284,288,292,304,316,320,325,332,333
%N A360554 Numbers > 1 whose unordered prime signature has non-integer median.
%C A360554 First differs from A187039 in having 2520 and lacking 1 and 12600.
%C A360554 A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.
%C A360554 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 A360554 The unordered prime signature of 2520 is {3,2,1,1}, with median 3/2, so 2520 is in the sequence.
%e A360554 The unordered prime signature of 12600 is {3,2,2,1}, with median 2, so 12600 is not in the sequence.
%t A360554 Select[Range[2,100],!IntegerQ[Median[Last/@FactorInteger[#]]]&]
%Y A360554 A subset of A030231.
%Y A360554 For mean instead of median we have A070011.
%Y A360554 Positions of odd terms in A360460.
%Y A360554 The complement is A360553 (without 1), counted by A360687.
%Y A360554 - For divisors (A063655) we have A139710, complement A139711.
%Y A360554 - For prime indices (A360005) we have A359912, complement A359908.
%Y A360554 - For distinct prime indices (A360457) we have A360551 complement A360550.
%Y A360554 - For distinct prime factors (A360458) we have A100367, complement A360552.
%Y A360554 - For prime factors (A360459) we have A072978, complement A359913.
%Y A360554 - For prime multiplicities (A360460) we have A360554, complement A360553.
%Y A360554 - For 0-prepended differences (A360555) we have A360557, complement A360556.
%Y A360554 A112798 lists prime indices, length A001222, sum A056239.
%Y A360554 A325347 = partitions w/ integer median, complement A307683, strict A359907.
%Y A360554 A326619/A326620 gives mean of distinct prime indices.
%Y A360554 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360554 Cf. A000975, A026424, A304038, A316413, A326621, A348551, A360006, A360009, A360248, A360453.
%K A360554 nonn
%O A360554 1,1
%A A360554 _Gus Wiseman_, Feb 16 2023