A255201 Number of prime factors of n^2.

0, 2, 2, 4, 2, 4, 2, 6, 4, 4, 2, 6, 2, 4, 4, 8, 2, 6, 2, 6, 4, 4, 2, 8, 4, 4, 6, 6, 2, 6, 2, 10, 4, 4, 4, 8, 2, 4, 4, 8, 2, 6, 2, 6, 6, 4, 2, 10, 4, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 8, 2, 4, 6, 12, 4, 6, 2, 6, 4, 6, 2, 10, 2, 4, 6, 6, 4, 6, 2, 10, 8, 4, 2, 8, 4, 4, 4, 8, 2, 8, 4, 6, 4, 4, 4, 12

Offset: 1

Author

Zak Seidov, Feb 17 2015

Keywords

• nonn

Comments

a(n) = 2 if n is prime.

All terms are even.

Record values are 2(m-1) for n = 2^m, m >= 0.

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000290, A001222.

Programs

Mathematica

Table[PrimeOmega[n^2], {n, 1000}] (* Indranil Ghosh, Mar 11 2017 *)

PARI

a(n) = bigomega(n^2); \\ Michel Marcus, Feb 17 2015

Formula

a(n) = A001222(n^2) = A001222(A000290(n)) = 2*A001222(n).