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

1,1

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

Links

Table of n, a(n) for n=1..61.

Example

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)

Mathematica

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

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.

Sequence in context: A229153 A119847 A279458 * A351295 A362606 A130092

Adjacent sequences: A119896 A119897 A119898 * A119900 A119901 A119902

Keyword

nonn

Author

Antti Karttunen, Jun 04 2006

Status

approved