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 A362616 #8 May 07 2023 08:38:42
%S A362616 2,3,4,5,7,8,9,11,13,16,17,18,19,23,25,27,29,31,32,37,41,43,47,49,50,
%T A362616 53,54,59,61,64,67,71,73,75,79,81,83,89,97,98,101,103,107,108,109,113,
%U A362616 121,125,127,128,131,137,139,147,149,150,151,157,162,163,167
%N A362616 Numbers in whose prime factorization the greatest factor is the unique mode.
%C A362616 First differs from A329131 in lacking 450 and having 1500.
%C A362616 A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes of {a,a,b,b,b,c,d,d,d} are {b,d}.
%e A362616 The factorization of 90 is 2*3*3*5, modes {3}, so 90 is missing.
%e A362616 The factorization of 450 is 2*3*3*5*5, modes {3,5}, so 450 is missing.
%e A362616 The factorization of 900 is 2*2*3*3*5*5, modes {2,3,5}, so 900 is missing.
%e A362616 The factorization of 1500 is 2*2*3*5*5*5, modes {5}, so 1500 is present.
%e A362616 The terms together with their prime indices begin:
%e A362616 2: {1} 27: {2,2,2} 67: {19}
%e A362616 3: {2} 29: {10} 71: {20}
%e A362616 4: {1,1} 31: {11} 73: {21}
%e A362616 5: {3} 32: {1,1,1,1,1} 75: {2,3,3}
%e A362616 7: {4} 37: {12} 79: {22}
%e A362616 8: {1,1,1} 41: {13} 81: {2,2,2,2}
%e A362616 9: {2,2} 43: {14} 83: {23}
%e A362616 11: {5} 47: {15} 89: {24}
%e A362616 13: {6} 49: {4,4} 97: {25}
%e A362616 16: {1,1,1,1} 50: {1,3,3} 98: {1,4,4}
%e A362616 17: {7} 53: {16} 101: {26}
%e A362616 18: {1,2,2} 54: {1,2,2,2} 103: {27}
%e A362616 19: {8} 59: {17} 107: {28}
%e A362616 23: {9} 61: {18} 108: {1,1,2,2,2}
%e A362616 25: {3,3} 64: {1,1,1,1,1,1} 109: {29}
%t A362616 prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
%t A362616 Select[Range[100],Commonest[prifacs[#]]=={Max[prifacs[#]]}&]
%Y A362616 First term with given bigomega is A000079.
%Y A362616 For median instead of mode we have A053263.
%Y A362616 Partitions of this type are counted by A362612.
%Y A362616 A112798 lists prime indices, length A001222, sum A056239.
%Y A362616 A356862 ranks partitions with a unique mode, counted by A362608.
%Y A362616 A359178 ranks partitions with a unique co-mode, counted by A362610.
%Y A362616 A362605 ranks partitions with more than one mode, counted by A362607.
%Y A362616 A362606 ranks partitions with more than one co-mode, counted by A362609.
%Y A362616 A362614 counts partitions by number of modes, ranked by A362611.
%Y A362616 A362615 counts partitions by number of co-modes, ranked by A362613.
%Y A362616 Cf. A000040, A002865, A327473, A327476, A358137, A360687.
%K A362616 nonn
%O A362616 1,1
%A A362616 _Gus Wiseman_, May 05 2023