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%I #16 Feb 01 2021 22:16:06
%S 10,21,22,34,39,46,55,57,62,82,85,87,91,94,111,115,118,129,133,134,
%T 146,155,159,166,183,187,194,203,205,206,213,218,235,237,247,253,254,
%U 259,267,274,295,298,301,303,314,321,334,335,339,341,358,365,371,377,382
%N Squarefree semiprimes whose prime indices sum to an even number.
%C A squarefree semiprime 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.
%e The sequence of terms together with their prime indices begins:
%e 10: {1,3} 115: {3,9} 213: {2,20}
%e 21: {2,4} 118: {1,17} 218: {1,29}
%e 22: {1,5} 129: {2,14} 235: {3,15}
%e 34: {1,7} 133: {4,8} 237: {2,22}
%e 39: {2,6} 134: {1,19} 247: {6,8}
%e 46: {1,9} 146: {1,21} 253: {5,9}
%e 55: {3,5} 155: {3,11} 254: {1,31}
%e 57: {2,8} 159: {2,16} 259: {4,12}
%e 62: {1,11} 166: {1,23} 267: {2,24}
%e 82: {1,13} 183: {2,18} 274: {1,33}
%e 85: {3,7} 187: {5,7} 295: {3,17}
%e 87: {2,10} 194: {1,25} 298: {1,35}
%e 91: {4,6} 203: {4,10} 301: {4,14}
%e 94: {1,15} 205: {3,13} 303: {2,26}
%e 111: {2,12} 206: {1,27} 314: {1,37}
%t Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&& EvenQ[Total[PrimePi/@First/@FactorInteger[#]]]&]
%Y A031215 looks at primes instead of semiprimes.
%Y A300061 and A319241 (squarefree) look all numbers (not just semiprimes).
%Y A338905 has this as union of even-indexed rows.
%Y A338906 is the nonsquarefree version.
%Y A338907 is the odd version.
%Y A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A005117 lists squarefree numbers.
%Y A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A024697 is the sum of semiprimes of weight n.
%Y A025129 is the sum of squarefree semiprimes of weight n.
%Y A056239 gives the sum of prime indices of n.
%Y A289182/A115392 list the positions of odd/even terms in A001358.
%Y A320656 counts factorizations into squarefree semiprimes.
%Y A332765 gives the greatest squarefree semiprime of weight n.
%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 A338904 groups semiprimes by weight.
%Y A338911 lists products of pairs of primes both of even index.
%Y A339114/A339115 give the least/greatest semiprime of weight n.
%Y A339116 groups squarefree semiprimes by greater prime factor.
%Y Cf. A000040, A001221, A001222, A087112, A098350, A112798, A168472, A338901, A338904, A339004, A339005.
%K nonn
%O 1,1
%A _Gus Wiseman_, Nov 28 2020
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