A192690 Nonprime numbers with a nonprime number of nonprime divisors.

1, 12, 16, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 68, 72, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 104, 108, 112, 116, 117, 124, 126, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 162, 164, 171, 172, 175, 176, 180, 184, 188

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 15 2011

Keywords

• nonn

Examples

			For example, 12 is composite and it has 6 divisors: 1, 2, 3, 4, 6, 12. Of these, 4 are not prime: 1, 4, 6, 12. Since 4 is not prime either, 12 is in the sequence.
		

Crossrefs

Cf. A139118, A141468, A167175.

Cf. A018252. - Omar E. Pol, Oct 20 2011

Programs

Mathematica

NonPrimeDivisors[n_] := Length[Select[Divisors[n], ! PrimeQ[#] &]]; Select[Range[200], ! PrimeQ[#] && ! PrimeQ[NonPrimeDivisors[#]] &] (* T. D. Noe, Oct 20 2011 *)

SageMath

def npd(n: int) -> int:
    return len([d for d in divisors(n) if not is_prime(d)])
def isA192690(n: int) -> bool:
    return not (is_prime(n) or is_prime(npd(n)))
A192690List = lambda b: [n for n in range(1, b) if isA192690(n)]
print(A192690List(189))  # Peter Luschny, Apr 22 2025