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%I #13 Dec 25 2020 20:08:19
%S 6,14,15,26,33,35,38,51,58,65,69,74,77,86,93,95,106,119,122,123,141,
%T 142,143,145,158,161,177,178,185,201,202,209,214,215,217,219,221,226,
%U 249,262,265,278,287,291,299,302,305,309,319,323,326,327,329,346,355
%N Semiprimes whose prime indices sum to an odd number.
%C All terms are squarefree (A005117).
%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.
%C The semiprimes in A300063; the semiprimes in A332820. - _Peter Munn_, Dec 25 2020
%F A338906 \/ A338907 = A001358.
%e The sequence of terms together with their prime indices begins:
%e 6: {1,2} 95: {3,8} 202: {1,26}
%e 14: {1,4} 106: {1,16} 209: {5,8}
%e 15: {2,3} 119: {4,7} 214: {1,28}
%e 26: {1,6} 122: {1,18} 215: {3,14}
%e 33: {2,5} 123: {2,13} 217: {4,11}
%e 35: {3,4} 141: {2,15} 219: {2,21}
%e 38: {1,8} 142: {1,20} 221: {6,7}
%e 51: {2,7} 143: {5,6} 226: {1,30}
%e 58: {1,10} 145: {3,10} 249: {2,23}
%e 65: {3,6} 158: {1,22} 262: {1,32}
%e 69: {2,9} 161: {4,9} 265: {3,16}
%e 74: {1,12} 177: {2,17} 278: {1,34}
%e 77: {4,5} 178: {1,24} 287: {4,13}
%e 86: {1,14} 185: {3,12} 291: {2,25}
%e 93: {2,11} 201: {2,19} 299: {6,9}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],PrimeOmega[#]==2&&OddQ[Total[primeMS[#]]]&]
%Y A031368 looks at primes instead of semiprimes.
%Y A098350 has this as union of odd-indexed antidiagonals.
%Y A300063 looks at all numbers (not just semiprimes).
%Y A338904 has this as union of odd-indexed rows.
%Y A338906 is the even version.
%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 A338908 lists squarefree semiprimes of even weight.
%Y A339114/A339115 give the least/greatest semiprime of weight n.
%Y Cf. A000040, A001222, A014342, A024697, A062198, A112798, A300061, A319242, A320655, A338910, A339003.
%Y Subsequence of A332820.
%K nonn
%O 1,1
%A _Gus Wiseman_, Nov 28 2020
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