This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364160 #13 Sep 18 2024 08:43:08
%S A364160 1,2,3,4,5,7,8,9,11,12,13,16,17,19,20,23,24,25,27,28,29,31,32,37,40,
%T A364160 41,43,44,45,47,48,49,52,53,56,59,60,61,63,64,67,68,71,72,73,76,79,80,
%U A364160 81,83,84,88,89,92,96,97,99,101,103,104,107,109,112,113,116
%N A364160 Numbers whose least prime factor has the greatest exponent.
%C A364160 First differs from A334298 in having 600 and lacking 180.
%C A364160 Also numbers whose minimum part in prime factorization is a unique mode.
%C A364160 If k is a term, then so are all powers of k. - _Robert Israel_, Sep 17 2024
%H A364160 Robert Israel, <a href="/A364160/b364160.txt">Table of n, a(n) for n = 1..10000</a>
%e A364160 The prime factorization of 600 is 2*2*2*3*5*5, and 3 > max(1,2), so 600 is in the sequence.
%e A364160 The prime factorization of 180 is 2*2*3*3*5, but 2 <= max(2,1), so 180 is not in the sequence.
%e A364160 The terms together with their prime indices begin:
%e A364160 1: {} 29: {10} 67: {19}
%e A364160 2: {1} 31: {11} 68: {1,1,7}
%e A364160 3: {2} 32: {1,1,1,1,1} 71: {20}
%e A364160 4: {1,1} 37: {12} 72: {1,1,1,2,2}
%e A364160 5: {3} 40: {1,1,1,3} 73: {21}
%e A364160 7: {4} 41: {13} 76: {1,1,8}
%e A364160 8: {1,1,1} 43: {14} 79: {22}
%e A364160 9: {2,2} 44: {1,1,5} 80: {1,1,1,1,3}
%e A364160 11: {5} 45: {2,2,3} 81: {2,2,2,2}
%e A364160 12: {1,1,2} 47: {15} 83: {23}
%e A364160 13: {6} 48: {1,1,1,1,2} 84: {1,1,2,4}
%e A364160 16: {1,1,1,1} 49: {4,4} 88: {1,1,1,5}
%e A364160 17: {7} 52: {1,1,6} 89: {24}
%e A364160 19: {8} 53: {16} 92: {1,1,9}
%e A364160 20: {1,1,3} 56: {1,1,1,4} 96: {1,1,1,1,1,2}
%e A364160 23: {9} 59: {17} 97: {25}
%e A364160 24: {1,1,1,2} 60: {1,1,2,3} 99: {2,2,5}
%e A364160 25: {3,3} 61: {18} 101: {26}
%e A364160 27: {2,2,2} 63: {2,2,4} 103: {27}
%e A364160 28: {1,1,4} 64: {1,1,1,1,1,1} 104: {1,1,1,6}
%p A364160 filter:= proc(n) local F,i;
%p A364160 F:= ifactors(n)[2];
%p A364160 if nops(F) = 1 then return true fi;
%p A364160 i:= min[index](F[..,1]);
%p A364160 andmap(t -> F[t,2] < F[i,2], {$1..nops(F)} minus {i})
%p A364160 end proc:
%p A364160 filter(1):= true:
%p A364160 select(filter, [$1..200]); # _Robert Israel_, Sep 17 2024
%t A364160 Select[Range[100],First[Last/@FactorInteger[#]] > Max@@Rest[Last/@FactorInteger[#]]&]
%Y A364160 Allowing any unique mode gives A356862, complement A362605.
%Y A364160 Allowing any unique co-mode gives A359178, complement A362606.
%Y A364160 The even case is A360013, counted by A241131.
%Y A364160 For greatest instead of least we have A362616, counted by A362612.
%Y A364160 These partitions are counted by A364193.
%Y A364160 A027746 lists prime factors (with multiplicity).
%Y A364160 A112798 lists prime indices, length A001222, sum A056239.
%Y A364160 A362611 counts modes in prime factorization, triangle A362614.
%Y A364160 A362613 counts co-modes in prime factorization, triangle A362615.
%Y A364160 A363486 gives least mode in prime indices, A363487 greatest.
%Y A364160 Cf. A098859, A327473, A327476, A360014, A360015, A362610, A364061, A364062.
%K A364160 nonn
%O A364160 1,2
%A A364160 _Gus Wiseman_, Jul 14 2023