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

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

filter:= n ->
   not isprime(n) and not isprime(nops(remove(isprime, NumberTheory:-Divisors(n)))):
select(filter, [$1..1000]); # Robert Israel, Jun 01 2026

Mathematica

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

Prog

(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

Crossrefs

Cf. A139118, A141468, A167175.

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

Includes A345381.

Sequence in context: A058080 A119911 A272861 * A382943 A378082 A064499

Adjacent sequences: A192687 A192688 A192689 * A192691 A192692 A192693

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 15 2011

Status

approved