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A362620 Numbers whose greatest prime factor is not a mode, meaning it appears fewer times than some other.

%I A362620 #12 Dec 15 2023 08:00:10
%S A362620 12,20,24,28,40,44,45,48,52,56,60,63,68,72,76,80,84,88,90,92,96,99,
%T A362620 104,112,116,117,120,124,126,132,135,136,140,144,148,152,153,156,160,
%U A362620 164,168,171,172,175,176,180,184,188,189,192,198,200,204,207,208,212
%N A362620 Numbers whose greatest prime factor is not a mode, meaning it appears fewer times than some other.
%C A362620 First differs from A112769 in lacking 300.
%H A362620 Robert Israel, <a href="/A362620/b362620.txt">Table of n, a(n) for n = 1..10000</a>
%H A362620 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mode_(statistics)">Mode (statistics)</a>.
%e A362620 The prime factorization of 90 is 2*3*3*5, with modes {3} and maximum 5, so 90 is in the sequence.
%p A362620 filter:= proc(n) local F;
%p A362620   F:= sort(ifactors(n)[2], (a,b) -> a[1]<b[1]);
%p A362620   F[-1,2] < max(F[..,2])
%p A362620 end proc:
%p A362620 select(filter, [$2..300]); # _Robert Israel_, Dec 15 2023
%t A362620 prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
%t A362620 Select[Range[2,100],FreeQ[Commonest[prifacs[#]],Max[prifacs[#]]]&]
%Y A362620 Partitions of this type are counted by A240302.
%Y A362620 The complement is A362619, counted by A171979.
%Y A362620 A027746 lists prime factors, A112798 indices, length A001222, sum A056239.
%Y A362620 A356862 ranks partitions with a unique mode, counted by A362608.
%Y A362620 A359178 ranks partitions with a unique co-mode, counted by A362610.
%Y A362620 A362605 ranks partitions with a more than one mode, counted by A362607.
%Y A362620 A362606 ranks partitions with a more than one co-mode, counted by A362609.
%Y A362620 A362611 counts modes in prime factorization, triangle version A362614.
%Y A362620 A362613 counts co-modes in prime factorization, triangle version A362615.
%Y A362620 A362621 ranks partitions with median equal to maximum, counted by A053263.
%Y A362620 Cf. A000040, A002865, A237824, A237984, A327473, A327476, A359908, A362616.
%K A362620 nonn
%O A362620 1,1
%A A362620 _Gus Wiseman_, May 11 2023