OFFSET
1,2
COMMENTS
Numbers m such that sigma(m) is a cube and (m is a cube or number of divisors of m is a multiple of 3). - Chai Wah Wu, Mar 10 2016
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..500
EXAMPLE
The divisors of 1164 are {1, 2, 3, 4, 6, 12, 97, 194, 291, 388, 582, 1164}. 1*2*3*4*6*12*97*194*291*388*582*1164 = 2487241979165915136 = 1354896^3 = (1164^2)^3. 1+2+3+4+6+12+97+194+291+388+582+1164 = 2744 = 14^3. Thus, since both the sum of divisors and the product of divisors are perfect cubes, 1164 is a member of this sequence.
PROG
(PARI) for(n=1, 10^6, d=divisors(n); s=sum(i=1, #d, d[i]); p=prod(j=1, #d, d[j]); if(ispower(s, 3)&&ispower(p, 3), print1(n, ", ")))
(Python)
from gmpy2 import iroot
from sympy import divisor_sigma
A244428_list = [i for i in range(1, 10**4) if (iroot(i, 3)[1] or not divisor_sigma(i, 0) % 3) and iroot(int(divisor_sigma(i, 1)), 3)[1]] # Chai Wah Wu, Mar 10 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Derek Orr, Jun 27 2014
STATUS
approved