cp's OEIS Frontend

A360457 Two times the median of the set of distinct prime indices of n; a(1) = 1.

%I A360457 #6 Feb 15 2023 21:48:23
%S A360457 1,2,4,2,6,3,8,2,4,4,10,3,12,5,5,2,14,3,16,4,6,6,18,3,6,7,4,5,20,4,22,
%T A360457 2,7,8,7,3,24,9,8,4,26,4,28,6,5,10,30,3,8,4,9,7,32,3,8,5,10,11,34,4,
%U A360457 36,12,6,2,9,4,38,8,11,6,40,3,42,13,5,9,9,4,44,4
%N A360457 Two times the median of the set of distinct prime indices of n; a(1) = 1.
%C A360457 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 A360457 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Distinct prime indices are listed by A304038.
%e A360457 The prime indices of 65 are {3,6}, with distinct parts {3,6}, with median 9/2, so a(65) = 9.
%e A360457 The prime indices of 900 are {1,1,2,2,3,3}, with distinct parts {1,2,3}, with median 2, so a(900) = 4.
%t A360457 Table[If[n==1,1,2*Median[PrimePi/@First/@FactorInteger[n]]],{n,100}]
%Y A360457 The version for divisors is A063655.
%Y A360457 For mean instead of two times median we have A326619/A326620.
%Y A360457 The version for all prime indices is A360005.
%Y A360457 Positions of first appearances are A360006, sorted A360007.
%Y A360457 The version for distinct prime factors is A360458.
%Y A360457 The version for all prime factors is A360459.
%Y A360457 The version for prime multiplicities is A360460.
%Y A360457 Positions of even terms are A360550.
%Y A360457 Positions of odd terms are A360551.
%Y A360457 The version for 0-prepended differences is A360555.
%Y A360457 A112798 lists prime indices, length A001222, sum A056239.
%Y A360457 A304038 lists distinct prime indices.
%Y A360457 A325347 counts partitions with integer median, complement A307683.
%Y A360457 A326567/A326568 gives mean of prime indices.
%Y A360457 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360457 Cf. A000975, A026424, A316413, A359907, A359908, A359912, A360248, A360453.
%K A360457 nonn
%O A360457 1,2
%A A360457 _Gus Wiseman_, Feb 14 2023