A325270 Numbers with 1 fewer distinct prime exponents than (not necessarily distinct) prime factors.

4, 6, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 28, 33, 34, 35, 38, 39, 44, 45, 46, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 68, 69, 74, 75, 76, 77, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 106, 111, 115, 116, 117, 118, 119, 121, 122, 123, 124, 129, 133

Offset

1,1

Comments

Also Heinz numbers of integer partitions with 1 fewer distinct multiplicities than parts, where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The enumeration of these partitions by sum is given by A117571.

Also numbers whose sorted prime signature is (1,1), (2), or (1,2). - Gus Wiseman, Jul 03 2019

Links

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

Example

The sequence of terms together with their prime indices begins:
    4: {1,1}
    6: {1,2}
    9: {2,2}
   10: {1,3}
   12: {1,1,2}
   14: {1,4}
   15: {2,3}
   18: {1,2,2}
   20: {1,1,3}
   21: {2,4}
   22: {1,5}
   25: {3,3}
   26: {1,6}
   28: {1,1,4}
   33: {2,5}
   34: {1,7}
   35: {3,4}
   38: {1,8}
   39: {2,6}
   44: {1,1,5}

Mathematica

Select[Range[100], PrimeOmega[#]==Length[Union[Last/@FactorInteger[#]]]+1&]

Crossrefs

Cf. A001221, A001222, A000961, A005117, A060687, A062770, A071625, A072774, A090858, A117571, A118914, A130091, A325244, A325259.

Sequence in context: A304634 A319240 A331051 * A051278 A328028 A366318

Adjacent sequences: A325267 A325268 A325269 * A325271 A325272 A325273

Keyword

nonn

Author

Gus Wiseman, Apr 18 2019

Status

approved