cp's OEIS Frontend

A362622 One and numbers whose prime factorization has its greatest part at a middle position.

%I A362622 #6 May 12 2023 12:22:45
%S A362622 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,25,26,27,29,31,
%T A362622 32,33,34,35,36,37,38,39,41,43,46,47,49,50,51,53,54,55,57,58,59,61,62,
%U A362622 64,65,67,69,71,73,74,75,77,79,81,82,83,85,86,87,89,91
%N A362622 One and numbers whose prime factorization has its greatest part at a middle position.
%e A362622 The prime factorization of 150 is 5*5*3*2, with middle parts {3,5}, so 150 is in the sequence.
%e A362622 The prime factorization of 90 is 5*3*3*2, with middle parts {3,3}, so 90 is not in the sequence.
%t A362622 mpm[q_]:=MemberQ[If[OddQ[Length[q]],{Median[q]},{q[[Length[q]/2]],q[[Length[q]/2+1]]}],Max@@q];
%t A362622 Select[Range[100],#==1||mpm[Flatten[Apply[ConstantArray,FactorInteger[#],{1}]]]&]
%Y A362622 Partitions of this type are counted by A237824.
%Y A362622 For modes instead of middles we have A362619, counted by A171979.
%Y A362622 The version for median instead of middles is A362621, counted by A053263.
%Y A362622 The complement for median is A362980, counted by A237821.
%Y A362622 A027746 lists prime factors, A112798 indices, length A001222, sum A056239.
%Y A362622 A362611 counts modes in prime factorization.
%Y A362622 A362613 counts co-modes in prime factorization.
%Y A362622 Cf. A000040, A002865, A237984, A327473, A327476, A359908, A362616, A362620.
%K A362622 nonn
%O A362622 1,2
%A A362622 _Gus Wiseman_, May 12 2023