A153147 a(n) = A007916(n)^3.

8, 27, 125, 216, 343, 1000, 1331, 1728, 2197, 2744, 3375, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 17576, 21952, 24389, 27000, 29791, 35937, 39304, 42875, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125, 97336, 103823

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 19 2008

Keywords

• nonn

Comments

2^3=8, 3^3=27, 4^3=64=2^6 is not in the sequence, 5^3=125, 6^3=216, ...

Crossrefs

Cf. A000578, A007916, A153157, A153158, A153159, A153160, A062838.

Programs

Mathematica

Select[Range[2,100],GCD@@Last/@FactorInteger@#==1&]^3

Python

from sympy import mobius, integer_nthroot
def A153147(n):
    def f(x): return int(n+1-sum(mobius(k)*(integer_nthroot(x,k)[0]-1) for k in range(2,x.bit_length())))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m**3

Extensions

Edited by Ray Chandler, Dec 22 2008