A229121 a(n) = Omega(n)^2 - omega(n)^2.

0, 0, 0, 3, 0, 0, 0, 8, 3, 0, 0, 5, 0, 0, 0, 15, 0, 5, 0, 5, 0, 0, 0, 12, 3, 0, 8, 5, 0, 0, 0, 24, 0, 0, 0, 12, 0, 0, 0, 12, 0, 0, 0, 5, 5, 0, 0, 21, 3, 5, 0, 5, 0, 12, 0, 12, 0, 0, 0, 7, 0, 0, 5, 35, 0, 0, 0, 5, 0, 0, 0, 21, 0, 0, 5, 5, 0, 0, 0, 21, 15, 0, 0

Offset: 1

Author

Wesley Ivan Hurt, Sep 17 2013

Keywords

• nonn
• easy

Comments

If n is squarefree, a(n) = 0. If n is a semiprime, then a(n) = 3 - 3 * mu(n).

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221 (omega), A001222 (Omega), A046660 (difference), A080256 (sum).

Programs

Maple

with(numtheory); A001221 := proc(n) nops(numtheory[factorset](n)) end: seq(bigomega(k)^2 - A001221(k)^2, k=1..100);

Mathematica

Table[PrimeOmega[n]^2 - PrimeNu[n]^2, {n, 100}] (* T. D. Noe, Sep 17 2013 *)

Formula

a(n) = A001222(n)^2 - A001221(n)^2.

a(n) = A046660(n) * A080256(n). - Amiram Eldar, Sep 16 2023