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%I #4 Dec 07 2020 01:48:53
%S 6,10,14,21,22,26,34,38,39,46,57,58,62,65,74,82,86,87,94,106,111,115,
%T 118,122,129,133,134,142,146,158,159,166,178,183,185,194,202,206,213,
%U 214,218,226,235,237,254,259,262,267,274,278,298,302,303,305,314,319
%N Numbers of the form prime(x) * prime(y) where x properly divides y. Squarefree semiprimes with divisible prime indices.
%C A squarefree semiprime (A006881) is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
%F Equals A318990 \ A000290.
%e The sequence of terms together with their prime indices begins:
%e 6: {1,2} 82: {1,13} 159: {2,16} 259: {4,12}
%e 10: {1,3} 86: {1,14} 166: {1,23} 262: {1,32}
%e 14: {1,4} 87: {2,10} 178: {1,24} 267: {2,24}
%e 21: {2,4} 94: {1,15} 183: {2,18} 274: {1,33}
%e 22: {1,5} 106: {1,16} 185: {3,12} 278: {1,34}
%e 26: {1,6} 111: {2,12} 194: {1,25} 298: {1,35}
%e 34: {1,7} 115: {3,9} 202: {1,26} 302: {1,36}
%e 38: {1,8} 118: {1,17} 206: {1,27} 303: {2,26}
%e 39: {2,6} 122: {1,18} 213: {2,20} 305: {3,18}
%e 46: {1,9} 129: {2,14} 214: {1,28} 314: {1,37}
%e 57: {2,8} 133: {4,8} 218: {1,29} 319: {5,10}
%e 58: {1,10} 134: {1,19} 226: {1,30} 321: {2,28}
%e 62: {1,11} 142: {1,20} 235: {3,15} 326: {1,38}
%e 65: {3,6} 146: {1,21} 237: {2,22} 334: {1,39}
%e 74: {1,12} 158: {1,22} 254: {1,31} 339: {2,30}
%t Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&& Divisible@@Reverse[PrimePi/@First/@FactorInteger[#]]&]
%Y A300912 is the version for relative primality.
%Y A318990 is the not necessarily squarefree version.
%Y A339002 is the version for non-relative primality.
%Y A339003 is the version for odd indices.
%Y A339004 is the version for even indices
%Y A001358 lists semiprimes.
%Y A005117 lists squarefree numbers.
%Y A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A320655 counts factorizations into semiprimes.
%Y A320656 counts factorizations into squarefree semiprimes.
%Y A338898/A338912/A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y Cf. A001221, A112798, A166237, A320911, A338901, A338904, A338909.
%K nonn
%O 1,1
%A _Gus Wiseman_, Dec 05 2020
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