A345381 Numbers with exactly 2 semiprime divisors.

12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 63, 68, 75, 76, 80, 88, 92, 96, 98, 99, 104, 112, 116, 117, 124, 135, 136, 147, 148, 152, 153, 160, 162, 164, 171, 172, 175, 176, 184, 188, 189, 192, 207, 208, 212, 224, 232, 236, 242, 244, 245, 248, 250, 261, 268, 272, 275

Offset: 1

Author

Wesley Ivan Hurt, Jun 16 2021

Keywords

• nonn

Comments

Numbers of the form p*q^k, where p and q are distinct primes and k>1.

Examples

			50 is in the sequence since it has exactly 2 semiprime divisors, 10 and 25.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (semiprimes).

Supersequence of A054753, A096156.

Programs

Mathematica

Select[Range[300], Length[(e = Sort[FactorInteger[#][[;; , 2]]])] == 2 && Min[e] == 1 && Max[e] > 1 &] (* Amiram Eldar, Sep 30 2021 *)

Python

from sympy import factorint
def ok(n):
    e = sorted(factorint(n).values())
    return len(e) == 2 and e[0] == 1 and e[1] > 1
print([k for k in range(276) if ok(k)]) # Michael S. Branicky, Dec 18 2021