A153157 a(n) = A007916(n)^4.

16, 81, 625, 1296, 2401, 10000, 14641, 20736, 28561, 38416, 50625, 83521, 104976, 130321, 160000, 194481, 234256, 279841, 331776, 456976, 614656, 707281, 810000, 923521, 1185921, 1336336, 1500625, 1874161, 2085136, 2313441, 2560000, 2825761

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 19 2008

Keywords

• nonn

Comments

2^4=16,3^4=81,4^4=256=2^8 is not in the sequence,5^4=625,6^4=1296,...

Crossrefs

Cf. A007916, A153147, A153158, A153159, A153160, A113849.

Programs

Mathematica

Select[Range[2,100],GCD@@Last/@FactorInteger@#==1&]^4

Python

from sympy import mobius, integer_nthroot
def A153157(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**4 # Chai Wah Wu, Nov 21 2024

Extensions

Edited by Ray Chandler, Dec 22 2008