A351416 Number of divisors of n that are either squarefree semiprimes, numbers of the form p^k (p prime, k>1), or numbers with at least one square divisor > 1 and 3 or more distinct prime factors.

0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 3, 0, 2, 0, 2, 1, 1, 0, 3, 1, 1, 2, 2, 0, 3, 0, 4, 1, 1, 1, 3, 0, 1, 1, 3, 0, 3, 0, 2, 2, 1, 0, 4, 1, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 5, 0, 1, 2, 5, 1, 3, 0, 2, 1, 3, 0, 4, 0, 1, 2, 2, 1, 3, 0, 4, 3, 1, 0, 5, 1, 1, 1, 3, 0, 5, 1, 2, 1, 1, 1

Offset

1,8

Links

Table of n, a(n) for n=1..95.

Formula

a(n) = Sum_{d|n} [[omega(d) = 2] = mu(d)^2], where [ ] is the Iverson bracket.

Example

a(60) = 5; 60 has divisors 6,10,15 (squarefree semiprimes), 4 (=2^2), and 60 = 2^2*3*5 (has at least 3 distinct prime factors and at least 1 square divisor > 1).

Crossrefs

Cf. A001221 (omega), A008683 (mu), A351414.

Sequence in context: A276806 A308427 A252736 * A253559 A136167 A140748

Adjacent sequences: A351413 A351414 A351415 * A351417 A351418 A351419

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 10 2022

Status

approved