cp's OEIS Frontend

A360006 Least positive integer whose prime indices have median n/2. a(1) = 1.

%I A360006 #5 Jan 24 2023 12:35:47
%S A360006 1,2,6,3,14,5,26,7,38,11,58,13,74,17,86,19,106,23,122,29,142,31,158,
%T A360006 37,178,41,202,43,214,47,226,53,262,59,278,61,302,67,326,71,346,73,
%U A360006 362,79,386,83,398,89,446,97,458,101,478,103,502,107,526,109,542,113
%N A360006 Least positive integer whose prime indices have median n/2. a(1) = 1.
%C A360006 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.
%C A360006 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%F A360006 Consists of 1 followed by A000040 interleaved with 2*A031215.
%t A360006 nn=100;
%t A360006 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360006 seq=Table[If[n==1,1,2*Median[prix[n]]],{n,nn}];
%t A360006 Table[Position[seq,k][[1,1]],{k,Count[Differences[Union[seq]],1]}]
%Y A360006 Position of first appearance of n in A360005.
%Y A360006 The sorted version is A360007, for mean A360008.
%Y A360006 A112798 lists prime indices, length A001222, sum A056239.
%Y A360006 A316413 lists numbers whose prime indices have integer mean.
%Y A360006 A325347 = partitions w/ integer median, strict A359907, complement A307683.
%Y A360006 A326567/A326568 gives mean of prime indices.
%Y A360006 A359893 counts partitions by median, cf. A359901, A359902.
%Y A360006 A359908 = numbers w/ integer median of prime indices, complement A359912.
%Y A360006 Cf. A026424, A359889, A359890, A360009.
%K A360006 nonn
%O A360006 1,2
%A A360006 _Gus Wiseman_, Jan 24 2023