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A325270
Numbers with 1 fewer distinct prime exponents than (not necessarily distinct) prime factors.
6
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
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&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 18 2019
STATUS
approved