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