A329717 a(n) is n (plus or minus) the number of distinct primes dividing n according to parity (even or odd).

1, 1, 2, 3, 4, 8, 6, 7, 8, 12, 10, 14, 12, 16, 17, 15, 16, 20, 18, 22, 23, 24, 22, 26, 24, 28, 26, 30, 28, 27, 30, 31, 35, 36, 37, 38, 36, 40, 41, 42, 40, 39, 42, 46, 47, 48, 46, 50, 48, 52, 53, 54, 52, 56, 57, 58, 59, 60, 58, 57, 60, 64, 65, 63, 67, 63, 66

Offset

1,3

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Formula

a(n) = n + A001221(n)*(-1)^A001221(n).

Example

A001221(3) = 1, so a(3) = 3-1 = 2. A001221(6) = 2, so a(6) = 6+2 = 8.

Mathematica

Array[# + (om = PrimeNu[#]) * (-1)^om &, 67] (* Amiram Eldar, Nov 23 2019 *)

Prog

(PARI) a(n) = my(om=omega(n)); n + (-1)^om*om; \\ Michel Marcus, Nov 20 2019

Crossrefs

Cf. A001221, A229109.

Sequence in context: A082313 A123494 A123716 * A229927 A222256 A367870

Adjacent sequences: A329714 A329715 A329716 * A329718 A329719 A329720

Keyword

nonn

Author

Lars Blomberg, Nov 20 2019

Status

approved