cp's OEIS Frontend

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

%I A367589 #5 Dec 01 2023 09:15:54
%S A367589 12,18,20,24,28,40,44,45,48,50,52,54,56,63,68,72,75,76,80,88,92,96,98,
%T A367589 99,104,108,112,116,117,124,135,136,144,147,148,152,153,160,162,164,
%U A367589 171,172,175,176,184,188,189,192,200,207,208,212,224,232,236,242,244
%N A367589 Numbers with exactly two distinct prime factors, both appearing with different exponents.
%C A367589 First differs from A177425 in lacking 360.
%C A367589 First differs from A182854 in lacking 360.
%C A367589 These are the Heinz numbers of the partitions counted by A182473.
%e A367589 The terms together with their prime indices begin:
%e A367589   12: {1,1,2}
%e A367589   18: {1,2,2}
%e A367589   20: {1,1,3}
%e A367589   24: {1,1,1,2}
%e A367589   28: {1,1,4}
%e A367589   40: {1,1,1,3}
%e A367589   44: {1,1,5}
%e A367589   45: {2,2,3}
%e A367589   48: {1,1,1,1,2}
%e A367589   50: {1,3,3}
%e A367589   52: {1,1,6}
%e A367589   54: {1,2,2,2}
%e A367589   56: {1,1,1,4}
%e A367589   63: {2,2,4}
%e A367589   68: {1,1,7}
%e A367589   72: {1,1,1,2,2}
%t A367589 Select[Range[100], PrimeNu[#]==2&&UnsameQ@@Last/@FactorInteger[#]&]
%Y A367589 The case of any multiplicities is A007774, counts A002133.
%Y A367589 These partitions are counted by A182473.
%Y A367589 The case of equal exponents is A367590, counts A367588.
%Y A367589 A000041 counts integer partitions, strict A000009.
%Y A367589 A091602 counts partitions by greatest multiplicity, least A243978.
%Y A367589 A098859 counts partitions with distinct multiplicities, ranks A130091.
%Y A367589 A116608 counts partitions by number of distinct parts.
%Y A367589 Cf. A071625, A072233, A072774, A109297, A367580.
%K A367589 nonn
%O A367589 1,1
%A A367589 _Gus Wiseman_, Dec 01 2023