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