A367589 Numbers with exactly two distinct prime factors, both appearing with different exponents.

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

Author

Gus Wiseman, Dec 01 2023

Keywords

• nonn

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.

Examples

			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}
		

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.

Cf. A071625, A072233, A072774, A109297, A367580.

Programs

Mathematica

Select[Range[100], PrimeNu[#]==2&&UnsameQ@@Last/@FactorInteger[#]&]