A334965 Numbers with strictly increasing prime multiplicities.

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, 50, 53, 54, 59, 61, 64, 67, 71, 73, 75, 79, 81, 83, 89, 97, 98, 101, 103, 107, 108, 109, 113, 121, 125, 127, 128, 131, 137, 139, 147, 149, 151, 157, 162, 163, 167, 169

Offset

1,2

Comments

First differs from A329131 in lacking 150.

Also numbers whose unsorted prime signature is strictly increasing.

Links

Table of n, a(n) for n=1..62.

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.

Cf. A000837, A032020, A098859, A100883, A329744, A332835, A333147, A333190.

Sequence in context: A166401 A329131 A362616 * A362621 A133811 A316525

Adjacent sequences: A334962 A334963 A334964 * A334966 A334967 A334968

Keyword

nonn

Author

Gus Wiseman, May 18 2020

Status

approved