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%I #14 Nov 27 2020 02:07:25
%S 21,39,57,65,87,91,111,115,129,133,159,183,185,203,213,235,237,247,
%T 259,267,299,301,303,305,319,321,339,365,371,377,393,417,427,445,453,
%U 481,489,497,515,517,519,543,551,553,559,565,579,597,611,623,669,685,687
%N Numbers of the form prime(x) * prime(y) where x and y are distinct and have a common divisor > 1.
%e The sequence of terms together with their prime indices begins:
%e 21: {2,4} 235: {3,15} 393: {2,32}
%e 39: {2,6} 237: {2,22} 417: {2,34}
%e 57: {2,8} 247: {6,8} 427: {4,18}
%e 65: {3,6} 259: {4,12} 445: {3,24}
%e 87: {2,10} 267: {2,24} 453: {2,36}
%e 91: {4,6} 299: {6,9} 481: {6,12}
%e 111: {2,12} 301: {4,14} 489: {2,38}
%e 115: {3,9} 303: {2,26} 497: {4,20}
%e 129: {2,14} 305: {3,18} 515: {3,27}
%e 133: {4,8} 319: {5,10} 517: {5,15}
%e 159: {2,16} 321: {2,28} 519: {2,40}
%e 183: {2,18} 339: {2,30} 543: {2,42}
%e 185: {3,12} 365: {3,21} 551: {8,10}
%e 203: {4,10} 371: {4,16} 553: {4,22}
%e 213: {2,20} 377: {6,10} 559: {6,14}
%t Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]
%Y A300912 is the complement in A001358.
%Y A338909 is the not necessarily squarefree version.
%Y A001358 lists semiprimes, with odd and even terms A046315 and A100484.
%Y A005117 lists squarefree numbers.
%Y A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A339005 lists products of pairs of distinct primes of divisible index.
%Y A320656 counts factorizations into squarefree semiprimes.
%Y A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A338910/A338911 list products of pairs of primes both of odd/even index.
%Y A339003/A339004 list squarefree semiprimes of odd/even index.
%Y Cf. A001221, A001222, A055684, A056239, A112798, A115392, A166237, A167171, A318990, A320892, A320911, A338901.
%K nonn
%O 1,1
%A _Gus Wiseman_, Nov 22 2020
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