A345446 Number of semiprime divisors of n whose square does not divide n.

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 1, 2, 0, 3, 0, 0, 1, 1, 1, 2, 0, 1, 1, 2, 0, 3, 0, 2, 2, 1, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 4, 0, 1, 2, 0, 1, 3, 0, 2, 1, 3, 0, 2, 0, 1, 2, 2, 1, 3, 0, 1, 0, 1, 0, 4, 1, 1, 1, 2, 0, 4, 1, 2, 1, 1

Offset: 1

Author

Wesley Ivan Hurt, Jun 19 2021

Keywords

• nonn

Comments

a(p) = 0 for p prime.

Crossrefs

Cf. A001358, A056595.

Programs

Mathematica

Table[Count[Select[Divisors[n],PrimeOmega[#]==2&],?(!IntegerQ[n/#^2]&)],{n,120}] (* _Harvey P. Dale, Aug 10 2023 *)

Formula

a(n) = Sum_{d|n} [Omega(d) = 2] * (ceiling(n/d^2) - floor(n/d^2)), where [ ] is the Iverson bracket.