A384500 Numbers k such that the parity of k and omega(k) are not equal.

1, 2, 4, 8, 15, 16, 21, 30, 32, 33, 35, 39, 42, 45, 51, 55, 57, 60, 63, 64, 65, 66, 69, 70, 75, 77, 78, 84, 85, 87, 90, 91, 93, 95, 99, 102, 110, 111, 114, 115, 117, 119, 120, 123, 126, 128, 129, 130, 132, 133, 135, 138, 140, 141, 143, 145, 147, 150, 153, 154, 155

Offset

1,2

Links

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

Formula

From Michael S. Branicky, May 31 2025: (Start)

{k | A000035(k) != A000035(A001221(k))}.

Union of A098904, A098905, and {1}. (End)

Example

1 is a term since 1 is odd and omega(1) = 0 (even).
8 is a term since 8 is even and omega(8) = 1 (odd).
15 is a term since 15 is odd and omega(15) = 2 (even).
56 is not a term since 56 is even and omega(56) = 2 (even).

Mathematica

Select[Range[155], OddQ[# - PrimeNu[#]] &] (* Amiram Eldar, May 31 2025 *)

Prog

(Python)
from sympy import factorint
def ok(n): return len(factorint(n))&1 != n&1
print([k for k in range(1, 156) if ok(k)]) # Michael S. Branicky, May 31 2025

Crossrefs

Cf. A000035, A001221, A098904, A098905.

Sequence in context: A002954 A019278 A267894 * A084345 A084561 A277166

Adjacent sequences: A384497 A384498 A384499 * A384501 A384502 A384503

Keyword

nonn,easy

Author

Guido Avagliano, May 31 2025

Extensions

Data corrected and extended by Michael S. Branicky, May 31 2025

Status

approved