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

6, 10, 14, 15, 21, 22, 24, 26, 33, 34, 35, 38, 39, 40, 46, 51, 54, 55, 56, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 95, 96, 104, 106, 111, 115, 118, 119, 122, 123, 126, 129, 132, 133, 134, 135, 136, 140, 141, 142, 143, 145, 146, 150

Offset: 1

Author

Antti Karttunen, Jun 04 2006

Keywords

• nonn

Comments

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

Examples

			From _Gus Wiseman_, Jun 20 2021: (Start)
The sequence of terms together with their prime indices begins:
       6: {1,2}          51: {2,7}          86: {1,14}
      10: {1,3}          54: {1,2,2,2}      87: {2,10}
      14: {1,4}          55: {3,5}          88: {1,1,1,5}
      15: {2,3}          56: {1,1,1,4}      90: {1,2,2,3}
      21: {2,4}          57: {2,8}          91: {4,6}
      22: {1,5}          58: {1,10}         93: {2,11}
      24: {1,1,1,2}      60: {1,1,2,3}      94: {1,15}
      26: {1,6}          62: {1,11}         95: {3,8}
      33: {2,5}          65: {3,6}          96: {1,1,1,1,1,2}
      34: {1,7}          69: {2,9}         104: {1,1,1,6}
      35: {3,4}          74: {1,12}        106: {1,16}
      38: {1,8}          77: {4,5}         111: {2,12}
      39: {2,6}          82: {1,13}        115: {3,9}
      40: {1,1,1,3}      84: {1,1,2,4}     118: {1,17}
      46: {1,9}          85: {3,7}         119: {4,7}
(End)
		

Crossrefs

Superset: A119847. Subset: A006881. The intersection of A028260 and A000037.

Positions of negative terms in A316524.

The partitions with these Heinz numbers are counted by A344608.

Complement of A344609.

Cf. A000041, A000070, A000097, A027187, A103919, A116406, A239829, A239830, A343941, A344607, A344651.

Programs

Mathematica

Select[Range[200],And@@EvenQ[{PrimeOmega[#],DivisorSigma[0,#]}]&] (* Harvey P. Dale, Jan 24 2013 *)