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a(n) = A007916(n)^4.
5

%I #10 Nov 22 2024 01:45:55

%S 16,81,625,1296,2401,10000,14641,20736,28561,38416,50625,83521,104976,

%T 130321,160000,194481,234256,279841,331776,456976,614656,707281,

%U 810000,923521,1185921,1336336,1500625,1874161,2085136,2313441,2560000,2825761

%N a(n) = A007916(n)^4.

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

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

%o (Python)

%o from sympy import mobius, integer_nthroot

%o def A153157(n):

%o def f(x): return int(n+1-sum(mobius(k)*(integer_nthroot(x,k)[0]-1) for k in range(2,x.bit_length())))

%o m, k = n, f(n)

%o while m != k: m, k = k, f(k)

%o return m**4 # _Chai Wah Wu_, Nov 21 2024

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

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 19 2008

%E Edited by _Ray Chandler_, Dec 22 2008