A346041 Numbers with exactly 1 semiprime divisor.

4, 6, 8, 9, 10, 14, 15, 16, 21, 22, 25, 26, 27, 32, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 64, 65, 69, 74, 77, 81, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 125, 128, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169

Offset: 1

Author

Wesley Ivan Hurt, Jul 02 2021

Keywords

• nonn

Comments

Numbers of the form p*q or p^k, where p and q are prime and k >= 2.

Numbers k such that A086971(k) = 1. - Wesley Ivan Hurt, Jun 21 2024

Examples

			6 is in the sequence since it has exactly 1 semiprime divisor, namely 6.
16 is in the sequence since it has exactly 1 semiprime divisor, namely 4.
		

Crossrefs

Cf. A001358 (semiprimes), A086971.

Programs

Mathematica

Select[Range@200,Length@Select[Divisors@#,PrimeOmega@#==2&]==1&] (* Giorgos Kalogeropoulos, Jul 03 2021 *)

PARI

isok(k) = sumdiv(k, d, bigomega(d)==2) == 1; \\ Michel Marcus, Jul 03 2021

Python

from sympy import factorint
def ok(n):
    f = factorint(n); w = len(f); W = sum(f.values())
    return (w == 1 and W >= 2) or (w == 2 and W == 2)
print(list(filter(ok, range(170)))) # Michael S. Branicky, Jul 03 2021