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A334965 Numbers with strictly increasing prime multiplicities.

%I A334965 #7 May 21 2020 21:19:18
%S A334965 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 A334965 50,53,54,59,61,64,67,71,73,75,79,81,83,89,97,98,101,103,107,108,109,
%U A334965 113,121,125,127,128,131,137,139,147,149,151,157,162,163,167,169
%N A334965 Numbers with strictly increasing prime multiplicities.
%C A334965 First differs from A329131 in lacking 150.
%C A334965 Also numbers whose unsorted prime signature is strictly increasing.
%e A334965 The sequence of terms together with their prime indices begins:
%e A334965     1: {}            25: {3,3}           64: {1,1,1,1,1,1}
%e A334965     2: {1}           27: {2,2,2}         67: {19}
%e A334965     3: {2}           29: {10}            71: {20}
%e A334965     4: {1,1}         31: {11}            73: {21}
%e A334965     5: {3}           32: {1,1,1,1,1}     75: {2,3,3}
%e A334965     7: {4}           37: {12}            79: {22}
%e A334965     8: {1,1,1}       41: {13}            81: {2,2,2,2}
%e A334965     9: {2,2}         43: {14}            83: {23}
%e A334965    11: {5}           47: {15}            89: {24}
%e A334965    13: {6}           49: {4,4}           97: {25}
%e A334965    16: {1,1,1,1}     50: {1,3,3}         98: {1,4,4}
%e A334965    17: {7}           53: {16}           101: {26}
%e A334965    18: {1,2,2}       54: {1,2,2,2}      103: {27}
%e A334965    19: {8}           59: {17}           107: {28}
%e A334965    23: {9}           61: {18}           108: {1,1,2,2,2}
%t A334965 Select[Range[100],Less@@Last/@FactorInteger[#]&]
%Y A334965 These are the Heinz numbers of the partitions counted by A100471.
%Y A334965 Partitions with strictly decreasing run-lengths are A100881.
%Y A334965 Partitions with weakly decreasing run-lengths are A100882.
%Y A334965 Partitions with weakly increasing run-lengths are A100883.
%Y A334965 The weakly decreasing version is A242031.
%Y A334965 The weakly increasing version is A304678.
%Y A334965 The strictly decreasing version is A304686.
%Y A334965 Compositions with strictly increasing or decreasing run-lengths are A333191.
%Y A334965 Cf. A000837, A032020, A098859, A100883, A329744, A332835, A333147, A333190.
%K A334965 nonn
%O A334965 1,2
%A A334965 _Gus Wiseman_, May 18 2020