cp's OEIS Frontend

A360459 Two times the median of the multiset of prime factors of n; a(1) = 2.

%I A360459 #7 Feb 15 2023 21:48:14
%S A360459 2,4,6,4,10,5,14,4,6,7,22,4,26,9,8,4,34,6,38,4,10,13,46,4,10,15,6,4,
%T A360459 58,6,62,4,14,19,12,5,74,21,16,4,82,6,86,4,6,25,94,4,14,10,20,4,106,6,
%U A360459 16,4,22,31,118,5,122,33,6,4,18,6,134,4,26,10,142,4,146
%N A360459 Two times the median of the multiset of prime factors of n; a(1) = 2.
%C A360459 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.
%e A360459 The prime factors of 60 are {2,2,3,5}, with median 5/2, so a(60) = 5.
%t A360459 Table[2*Median[Join@@ConstantArray@@@FactorInteger[n]],{n,100}]
%Y A360459 The union is 2 followed by A014091, complement of A014092.
%Y A360459 The prime factors themselves are listed by A027746, distinct A027748.
%Y A360459 The version for divisors is A063655.
%Y A360459 Positions of odd terms are A072978 (except 1).
%Y A360459 For mean instead of twice median: A123528/A123529, distinct A323171/A323172.
%Y A360459 Positions of even terms are A359913 (and 1).
%Y A360459 The version for prime indices is A360005.
%Y A360459 The version for distinct prime indices is A360457.
%Y A360459 The version for distinct prime factors is A360458.
%Y A360459 The version for prime multiplicities is A360460.
%Y A360459 The version for 0-prepended differences is A360555.
%Y A360459 A112798 lists prime indices, length A001222, sum A056239.
%Y A360459 A325347 counts partitions with integer median, complement A307683.
%Y A360459 A326567/A326568 gives mean of prime indices.
%Y A360459 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360459 Cf. A000975, A026424, A027336, A078174, A316413, A359907, A359908, A360006, A360007, A360248, A360552.
%K A360459 nonn
%O A360459 1,1
%A A360459 _Gus Wiseman_, Feb 14 2023