OFFSET
1,2
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
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
EXAMPLE
The set of proper divisors of 8 is {1,2,4} and 1*2*4 = 2^3 so 8 is in the sequence.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Derek Orr, Oct 04 2013
EXTENSIONS
Corrected and edited by Farideh Firoozbakht Oct 10 2013
STATUS
approved