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a(n) = A007916(n)^6.
5

%I #11 Nov 22 2024 01:48:41

%S 64,729,15625,46656,117649,1000000,1771561,2985984,4826809,7529536,

%T 11390625,24137569,34012224,47045881,64000000,85766121,113379904,

%U 148035889,191102976,308915776,481890304,594823321,729000000,887503681

%N a(n) = A007916(n)^6.

%t Select[Range[2,100],GCD@@Last/@FactorInteger@#==1&]^6

%o (Python)

%o from sympy import mobius, integer_nthroot

%o def A153160(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**6 # _Chai Wah Wu_, Nov 21 2024

%Y Cf. A007916, A153147, A153157, A153158, A153159, A113851.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 19 2008

%E Edited and extended by _Ray Chandler_, Dec 22 2008