cp's OEIS Frontend

A360553 Numbers > 1 whose unordered prime signature has integer median.

%I A360553 #8 Feb 16 2023 13:41:49
%S A360553 2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,21,22,23,24,25,26,27,29,30,
%T A360553 31,32,33,34,35,36,37,38,39,40,41,42,43,46,47,49,51,53,54,55,56,57,58,
%U A360553 59,60,61,62,64,65,66,67,69,70,71,73,74,77,78,79,81,82,83
%N A360553 Numbers > 1 whose unordered prime signature has integer median.
%C A360553 First differs from A067340 in having 60.
%C A360553 A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.
%C A360553 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 A360553 The unordered prime signature of 60 is {1,1,2}, with median 1, so 60 is in the sequence.
%e A360553 The unordered prime signature of 1260 is {1,1,2,2}, with median 3/2, so 1260 is not in the sequence.
%t A360553 Select[Range[2,100],IntegerQ[Median[Last/@FactorInteger[#]]]&]
%Y A360553 For mean instead of median we have A067340, complement A070011.
%Y A360553 Positions of even terms in A360460.
%Y A360553 The complement is A360554 (without 1).
%Y A360553 These partitions are counted by A360687.
%Y A360553 - For divisors (A063655) we have A139711, complement A139710.
%Y A360553 - For prime indices (A360005) we have A359908, complement A359912.
%Y A360553 - For distinct prime indices (A360457) we have A360550, complement A360551.
%Y A360553 - For distinct prime factors (A360458) we have A360552, complement A100367.
%Y A360553 - For prime factors (A360459) we have A359913, complement A072978.
%Y A360553 - For prime multiplicities (A360460) we have A360553, complement A360554.
%Y A360553 - For 0-prepended differences (A360555) we have A360556, complement A360557.
%Y A360553 A112798 lists prime indices, length A001222, sum A056239.
%Y A360553 A124010 lists prime signature.
%Y A360553 A325347 = partitions w/ integer median, complement A307683, strict A359907.
%Y A360553 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360553 A360454 = numbers whose prime indices and signature have the same median.
%Y A360553 Cf. A000975, A026424, A078174, A078175, A316413, A326621, A360453.
%K A360553 nonn
%O A360553 1,1
%A A360553 _Gus Wiseman_, Feb 16 2023