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A119899 Integers i such that bigomega(i) (A001222) and tau(i) (A000005) are both even.

%I A119899 #8 Jun 21 2021 00:05:49
%S A119899 6,10,14,15,21,22,24,26,33,34,35,38,39,40,46,51,54,55,56,57,58,60,62,
%T A119899 65,69,74,77,82,84,85,86,87,88,90,91,93,94,95,96,104,106,111,115,118,
%U A119899 119,122,123,126,129,132,133,134,135,136,140,141,142,143,145,146,150
%N A119899 Integers i such that bigomega(i) (A001222) and tau(i) (A000005) are both even.
%C A119899 Also numbers whose alternating sum of prime indices is < 0. Equivalently, numbers with even bigomega whose conjugate prime indices are not all even. This is the intersection of A028260 and A000037. - _Gus Wiseman_, Jun 20 2021
%e A119899 From _Gus Wiseman_, Jun 20 2021: (Start)
%e A119899 The sequence of terms together with their prime indices begins:
%e A119899        6: {1,2}          51: {2,7}          86: {1,14}
%e A119899       10: {1,3}          54: {1,2,2,2}      87: {2,10}
%e A119899       14: {1,4}          55: {3,5}          88: {1,1,1,5}
%e A119899       15: {2,3}          56: {1,1,1,4}      90: {1,2,2,3}
%e A119899       21: {2,4}          57: {2,8}          91: {4,6}
%e A119899       22: {1,5}          58: {1,10}         93: {2,11}
%e A119899       24: {1,1,1,2}      60: {1,1,2,3}      94: {1,15}
%e A119899       26: {1,6}          62: {1,11}         95: {3,8}
%e A119899       33: {2,5}          65: {3,6}          96: {1,1,1,1,1,2}
%e A119899       34: {1,7}          69: {2,9}         104: {1,1,1,6}
%e A119899       35: {3,4}          74: {1,12}        106: {1,16}
%e A119899       38: {1,8}          77: {4,5}         111: {2,12}
%e A119899       39: {2,6}          82: {1,13}        115: {3,9}
%e A119899       40: {1,1,1,3}      84: {1,1,2,4}     118: {1,17}
%e A119899       46: {1,9}          85: {3,7}         119: {4,7}
%e A119899 (End)
%t A119899 Select[Range[200],And@@EvenQ[{PrimeOmega[#],DivisorSigma[0,#]}]&] (* _Harvey P. Dale_, Jan 24 2013 *)
%Y A119899 Superset: A119847. Subset: A006881. The intersection of A028260 and A000037.
%Y A119899 Positions of negative terms in A316524.
%Y A119899 The partitions with these Heinz numbers are counted by A344608.
%Y A119899 Complement of A344609.
%Y A119899 Cf. A000041, A000070, A000097, A027187, A103919, A116406, A239829, A239830, A343941, A344607, A344651.
%K A119899 nonn
%O A119899 1,1
%A A119899 _Antti Karttunen_, Jun 04 2006