%I #9 Nov 29 2020 21:56:11
%S 4,9,10,21,22,25,34,39,46,49,55,57,62,82,85,87,91,94,111,115,118,121,
%T 129,133,134,146,155,159,166,169,183,187,194,203,205,206,213,218,235,
%U 237,247,253,254,259,267,274,289,295,298,301,303,314,321,334,335,339
%N Semiprimes whose prime indices sum to an even number.
%C A semiprime is a product of any two 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 A338906 \/ A338907 = A001358.
%e The sequence of terms together with their prime indices begins:
%e 4: {1,1} 87: {2,10} 183: {2,18} 274: {1,33}
%e 9: {2,2} 91: {4,6} 187: {5,7} 289: {7,7}
%e 10: {1,3} 94: {1,15} 194: {1,25} 295: {3,17}
%e 21: {2,4} 111: {2,12} 203: {4,10} 298: {1,35}
%e 22: {1,5} 115: {3,9} 205: {3,13} 301: {4,14}
%e 25: {3,3} 118: {1,17} 206: {1,27} 303: {2,26}
%e 34: {1,7} 121: {5,5} 213: {2,20} 314: {1,37}
%e 39: {2,6} 129: {2,14} 218: {1,29} 321: {2,28}
%e 46: {1,9} 133: {4,8} 235: {3,15} 334: {1,39}
%e 49: {4,4} 134: {1,19} 237: {2,22} 335: {3,19}
%e 55: {3,5} 146: {1,21} 247: {6,8} 339: {2,30}
%e 57: {2,8} 155: {3,11} 253: {5,9} 341: {5,11}
%e 62: {1,11} 159: {2,16} 254: {1,31} 358: {1,41}
%e 82: {1,13} 166: {1,23} 259: {4,12} 361: {8,8}
%e 85: {3,7} 169: {6,6} 267: {2,24} 365: {3,21}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],PrimeOmega[#]==2&&EvenQ[Total[primeMS[#]]]&]
%Y A031215 looks at primes instead of semiprimes.
%Y A098350 has this as union of even-indexed antidiagonals.
%Y A300061 looks at all numbers (not just semiprimes).
%Y A338904 has this as union of even-indexed rows.
%Y A338907 is the odd version.
%Y A338908 is the squarefree case.
%Y A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A056239 gives the sum of prime indices (Heinz weight).
%Y A084126 and A084127 give the prime factors of semiprimes.
%Y A087112 groups semiprimes by greater factor.
%Y A289182/A115392 list the positions of odd/even terms in A001358.
%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 A338911 lists products of pairs of primes both of even index.
%Y A339114/A339115 give the least/greatest semiprime of weight n.
%Y Cf. A000040, A001222, A024697, A037143, A112798, A300063, A319242, A320655, A332765, A338910, A339004.
%K nonn
%O 1,1
%A _Gus Wiseman_, Nov 28 2020