A229972 - OEIS

%I #33 Jul 07 2022 06:42:29

%S 1,8,16,24,27,30,40,42,54,56,64,66,70,78,81,88,102,104,105,110,114,

%T 125,128,130,135,136,138,152,154,165,170,174,182,184,186,189,190,192,

%U 195,216,222,230,231,232,238,240,246,248,250,255,258,266,273,282,285

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

%C 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

%H Chai Wah Wu, <a href="/A229972/b229972.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Select[Range[343],!PrimeQ[#]&&IntegerQ[(Apply[Times,Divisors[#]]/#)^(1/3)]&] (* _Farideh Firoozbakht_ Oct 10 2013 *)

%t Select[Range[300],!PrimeQ[#]&&IntegerQ[Surd[Times@@Most[Divisors[ #]],3]]&] (* _Harvey P. Dale_, Oct 24 2017 *)

%t m = 7; Union[Range[m]^3, Select[Range[m^3], !PrimeQ[#] && Mod[DivisorSigma[0, #], 3] == 2 &]] (* _Amiram Eldar_, Jul 07 2022 *)

%o (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,", ")))

%o (Python)

%o from gmpy2 import iroot

%o from sympy import divisor_count, isprime

%o 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

%Y Cf. A007956.

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

%K nonn,easy

%O 1,2

%A _Derek Orr_, Oct 04 2013

%E Corrected and edited by _Farideh Firoozbakht_ Oct 10 2013