cp's OEIS Frontend

A360460 Two times the median of the unordered prime signature of n; a(1) = 1.

%I A360460 #5 Feb 16 2023 09:04:19
%S A360460 1,2,2,4,2,2,2,6,4,2,2,3,2,2,2,8,2,3,2,3,2,2,2,4,4,2,6,3,2,2,2,10,2,2,
%T A360460 2,4,2,2,2,4,2,2,2,3,3,2,2,5,4,3,2,3,2,4,2,4,2,2,2,2,2,2,3,12,2,2,2,3,
%U A360460 2,2,2,5,2,2,3,3,2,2,2,5,8,2,2,2,2,2,2
%N A360460 Two times the median of the unordered prime signature of n; a(1) = 1.
%C A360460 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length). Since the denominator is always 1 or 2, the median can be represented as an integer by multiplying by 2.
%C A360460 A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.
%e A360460 The unordered prime signature of 2520 is {1,1,2,3}, with median 3/2, so a(2520) = 3.
%t A360460 Table[If[n==1,1,2*Median[Last/@FactorInteger[n]]],{n,100}]
%Y A360460 The version for divisors is A063655.
%Y A360460 For mean instead of two times median we have A088529/A088530.
%Y A360460 Prime signature is A124010, unordered A118914.
%Y A360460 The version for prime indices is A360005.
%Y A360460 The version for distinct prime indices is A360457.
%Y A360460 The version for distinct prime factors is A360458.
%Y A360460 The version for prime factors is A360459.
%Y A360460 Positions of even terms are A360553.
%Y A360460 Positions of odd terms are A360554.
%Y A360460 The version for 0-prepended differences is A360555.
%Y A360460 A112798 lists prime indices, length A001222, sum A056239.
%Y A360460 A304038 lists distinct prime indices.
%Y A360460 A325347 counts partitions w/ integer median, complement A307683.
%Y A360460 A329976 counts partitions with median multiplicity 1.
%Y A360460 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360460 Cf. A000975, A026424, A133464, A359907, A359908, A360454.
%K A360460 nonn
%O A360460 1,2
%A A360460 _Gus Wiseman_, Feb 14 2023