A362619 - OEIS

%I #7 May 11 2023 08:47:12

%S 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 31,32,33,34,35,36,37,38,39,41,42,43,46,47,49,50,51,53,54,55,57,58,59,

%U 61,62,64,65,66,67,69,70,71,73,74,75,77,78,79,81,82,83

%N 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 First differs from A304678 in having 300.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Mode_(statistics)">Mode (statistics)</a>.

%e 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 prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];

%t Select[Range[100],MemberQ[Commonest[prifacs[#]],Max[prifacs[#]]&]

%Y Partitions of this type are counted by A171979.

%Y The case of a unique mode is A362616, counted by A362612.

%Y The complement is A362620, counted by A240302.

%Y A027746 lists prime factors, A112798 indices, length A001222, sum A056239.

%Y A356862 ranks partitions with a unique mode, counted by A362608.

%Y A359178 ranks partitions with a unique co-mode, counted by A362610.

%Y A362605 ranks partitions with a more than one mode, counted by A362607.

%Y A362606 ranks partitions with a more than one co-mode, counted by A362609.

%Y A362611 counts modes in prime factorization, triangle version A362614.

%Y A362613 counts co-modes in prime factorization, triangle version A362615.

%Y A362621 ranks partitions with median equal to maximum, counted by A053263.

%Y Cf. A000040, A002865, A237824, A237984, A327473, A327476, A359908.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 09 2023