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A367589
Numbers with exactly two distinct prime factors, both appearing with different exponents.
2
12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 63, 68, 72, 75, 76, 80, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 124, 135, 136, 144, 147, 148, 152, 153, 160, 162, 164, 171, 172, 175, 176, 184, 188, 189, 192, 200, 207, 208, 212, 224, 232, 236, 242, 244
OFFSET
1,1
COMMENTS
First differs from A177425 in lacking 360.
First differs from A182854 in lacking 360.
These are the Heinz numbers of the partitions counted by A182473.
EXAMPLE
The terms together with their prime indices begin:
12: {1,1,2}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
28: {1,1,4}
40: {1,1,1,3}
44: {1,1,5}
45: {2,2,3}
48: {1,1,1,1,2}
50: {1,3,3}
52: {1,1,6}
54: {1,2,2,2}
56: {1,1,1,4}
63: {2,2,4}
68: {1,1,7}
72: {1,1,1,2,2}
MATHEMATICA
Select[Range[100], PrimeNu[#]==2&&UnsameQ@@Last/@FactorInteger[#]&]
CROSSREFS
The case of any multiplicities is A007774, counts A002133.
These partitions are counted by A182473.
The case of equal exponents is A367590, counts A367588.
A000041 counts integer partitions, strict A000009.
A091602 counts partitions by greatest multiplicity, least A243978.
A098859 counts partitions with distinct multiplicities, ranks A130091.
A116608 counts partitions by number of distinct parts.
Sequence in context: A317616 A375934 A332785 * A177425 A182854 A348097
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 01 2023
STATUS
approved