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

1,1

Comments

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

Links

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

Formula

a(n) ~ k*n log n where k = 1/A136141 = 1.293398.... - Charles R Greathouse IV, Feb 04 2026

Example

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

Mathematica

Select[Range[300], Length[(e = Sort[FactorInteger[#][[;; , 2]]])] == 2 && Min[e] == 1 && Max[e] > 1 &] (* Amiram Eldar, Sep 30 2021 *)
Select[Range[300], Count[Divisors[#], _?(PrimeOmega[#]==2&)]==2&] (* Harvey P. Dale, Mar 16 2026 *)

Prog

(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
(PARI) list(lim)=my(v=List()); for(e=2, logint(lim\3, 2), forprime(p=2, logint(lim\2, e), my(pe=p^e); forprime(q=2, lim\pe, if(p!=q, listput(v, pe*q))))); Set(v) \\ Charles R Greathouse IV, Feb 04 2026

Crossrefs

Supersequence of A054753, A096156.

Cf. A001358 (semiprimes).

Sequence in context: A182854 A348097 A394860 * A328930 A392537 A389227

Adjacent sequences: A345378 A345379 A345380 * A345382 A345383 A345384

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 16 2021

Status

approved