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%I A362619 #7 May 11 2023 08:47:12
%S A362619 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,25,26,27,29,30,
%T A362619 31,32,33,34,35,36,37,38,39,41,42,43,46,47,49,50,51,53,54,55,57,58,59,
%U A362619 61,62,64,65,66,67,69,70,71,73,74,75,77,78,79,81,82,83
%N A362619 One and all numbers whose greatest prime factor is a mode, meaning it appears at least as many times as each of the others.
%C A362619 First differs from A304678 in having 300.
%H A362619 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mode_(statistics)">Mode (statistics)</a>.
%e A362619 The prime factorization of 300 is 2*2*3*5*5, with modes {2,5} and maximum 5, so 300 is in the sequence.
%t A362619 prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
%t A362619 Select[Range[100],MemberQ[Commonest[prifacs[#]],Max[prifacs[#]]&]
%Y A362619 Partitions of this type are counted by A171979.
%Y A362619 The case of a unique mode is A362616, counted by A362612.
%Y A362619 The complement is A362620, counted by A240302.
%Y A362619 A027746 lists prime factors, A112798 indices, length A001222, sum A056239.
%Y A362619 A356862 ranks partitions with a unique mode, counted by A362608.
%Y A362619 A359178 ranks partitions with a unique co-mode, counted by A362610.
%Y A362619 A362605 ranks partitions with a more than one mode, counted by A362607.
%Y A362619 A362606 ranks partitions with a more than one co-mode, counted by A362609.
%Y A362619 A362611 counts modes in prime factorization, triangle version A362614.
%Y A362619 A362613 counts co-modes in prime factorization, triangle version A362615.
%Y A362619 A362621 ranks partitions with median equal to maximum, counted by A053263.
%Y A362619 Cf. A000040, A002865, A237824, A237984, A327473, A327476, A359908.
%K A362619 nonn
%O A362619 1,2
%A A362619 _Gus Wiseman_, May 09 2023

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