OFFSET
1,2
COMMENTS
First differs from A329131 in lacking 150.
Also numbers whose unsorted prime signature is strictly increasing.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {} 25: {3,3} 64: {1,1,1,1,1,1}
2: {1} 27: {2,2,2} 67: {19}
3: {2} 29: {10} 71: {20}
4: {1,1} 31: {11} 73: {21}
5: {3} 32: {1,1,1,1,1} 75: {2,3,3}
7: {4} 37: {12} 79: {22}
8: {1,1,1} 41: {13} 81: {2,2,2,2}
9: {2,2} 43: {14} 83: {23}
11: {5} 47: {15} 89: {24}
13: {6} 49: {4,4} 97: {25}
16: {1,1,1,1} 50: {1,3,3} 98: {1,4,4}
17: {7} 53: {16} 101: {26}
18: {1,2,2} 54: {1,2,2,2} 103: {27}
19: {8} 59: {17} 107: {28}
23: {9} 61: {18} 108: {1,1,2,2,2}
MATHEMATICA
Select[Range[100], Less@@Last/@FactorInteger[#]&]
CROSSREFS
These are the Heinz numbers of the partitions counted by A100471.
Partitions with strictly decreasing run-lengths are A100881.
Partitions with weakly decreasing run-lengths are A100882.
Partitions with weakly increasing run-lengths are A100883.
The weakly decreasing version is A242031.
The weakly increasing version is A304678.
The strictly decreasing version is A304686.
Compositions with strictly increasing or decreasing run-lengths are A333191.
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2020
STATUS
approved