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%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