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 A362621 #7 May 12 2023 09:13:45
%S A362621 1,2,3,4,5,7,8,9,11,13,16,17,18,19,23,25,27,29,31,32,37,41,43,47,49,
%T A362621 50,53,54,59,61,64,67,71,73,75,79,81,83,89,97,98,101,103,107,108,109,
%U A362621 113,121,125,127,128,131,137,139,147,149,151,157,162,163,167,169
%N A362621 One and numbers whose multiset of prime factors (with multiplicity) has the same median as maximum.
%C A362621 First differs from A334965 in having 750 and lacking 2250.
%C A362621 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%e A362621 The prime factorization of 108 is 2*2*3*3*3, and the multiset {2,2,3,3,3} has median 3 and maximum 3, so 108 is in the sequence.
%e A362621 The prime factorization of 2250 is 2*3*3*5*5*5, and the multiset {2,3,3,5,5,5} has median 4 and maximum 5, so 2250 is not in the sequence.
%e A362621 The terms together with their prime indices begin:
%e A362621 1: {} 25: {3,3} 64: {1,1,1,1,1,1}
%e A362621 2: {1} 27: {2,2,2} 67: {19}
%e A362621 3: {2} 29: {10} 71: {20}
%e A362621 4: {1,1} 31: {11} 73: {21}
%e A362621 5: {3} 32: {1,1,1,1,1} 75: {2,3,3}
%e A362621 7: {4} 37: {12} 79: {22}
%e A362621 8: {1,1,1} 41: {13} 81: {2,2,2,2}
%e A362621 9: {2,2} 43: {14} 83: {23}
%e A362621 11: {5} 47: {15} 89: {24}
%e A362621 13: {6} 49: {4,4} 97: {25}
%e A362621 16: {1,1,1,1} 50: {1,3,3} 98: {1,4,4}
%e A362621 17: {7} 53: {16} 101: {26}
%e A362621 18: {1,2,2} 54: {1,2,2,2} 103: {27}
%e A362621 19: {8} 59: {17} 107: {28}
%e A362621 23: {9} 61: {18} 108: {1,1,2,2,2}
%t A362621 Select[Range[100],(y=Flatten[Apply[ConstantArray,FactorInteger[#],{1}]];Max@@y==Median[y])&]
%Y A362621 Partitions of this type are counted by A053263.
%Y A362621 For mode instead of median we have A362619, counted by A171979.
%Y A362621 For parts at middle position (instead of median) we have A362622.
%Y A362621 The complement is A362980, counted by A237821.
%Y A362621 A027746 lists prime factors, A112798 indices, length A001222, sum A056239.
%Y A362621 A362611 counts modes in prime factorization, triangle version A362614.
%Y A362621 A362613 counts co-modes in prime factorization, triangle version A362615.
%Y A362621 Cf. A000040, A002865, A237824, A327473, A327476, A359908, A362616, A362620.
%K A362621 nonn
%O A362621 1,2
%A A362621 _Gus Wiseman_, May 12 2023