A229972 Nonprime numbers whose product of proper divisors is a perfect cube.

1, 8, 16, 24, 27, 30, 40, 42, 54, 56, 64, 66, 70, 78, 81, 88, 102, 104, 105, 110, 114, 125, 128, 130, 135, 136, 138, 152, 154, 165, 170, 174, 182, 184, 186, 189, 190, 192, 195, 216, 222, 230, 231, 232, 238, 240, 246, 248, 250, 255, 258, 266, 273, 282, 285

Offset: 1

Author

Derek Orr, Oct 04 2013

Keywords

• nonn
• easy

Comments

A nonprime number m is a term if and only if m is a cube or the number of divisors of m is of the form 3k+2. - Chai Wah Wu, Mar 09 2016

Examples

			The set of proper divisors of 8 is {1,2,4} and 1*2*4 = 2^3 so 8 is in the sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007956.

Union of A000578 and (intersection of A002808 and A211338).

Programs

Mathematica

Select[Range[343],!PrimeQ[#]&&IntegerQ[(Apply[Times,Divisors[#]]/#)^(1/3)]&] (* Farideh Firoozbakht Oct 10 2013 *)
Select[Range[300],!PrimeQ[#]&&IntegerQ[Surd[Times@@Most[Divisors[ #]],3]]&] (* Harvey P. Dale, Oct 24 2017 *)
m = 7; Union[Range[m]^3, Select[Range[m^3], !PrimeQ[#] && Mod[DivisorSigma[0, #], 3] == 2 &]] (* Amiram Eldar, Jul 07 2022 *)

PARI

for(n=1,10^3,d=divisors(n);p=prod(i=1,#d-1,d[i]);if(p!=1&&ispower(p,3),print1(n,", ")))

Python

from gmpy2 import iroot
from sympy import divisor_count, isprime
A229972_list = [i for i in range(1,10**3) if not isprime(i) and (iroot(i,3)[1] or divisor_count(i) % 3 == 2)] # Chai Wah Wu, Mar 10 2016

Extensions

Corrected and edited by Farideh Firoozbakht Oct 10 2013