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%I #7 Mar 18 2021 22:58:19
%S 1,-1,-1,0,-1,0,-1,1,0,0,-1,0,-1,1,1,0,-1,0,-1,0,1,0,-1,0,1,1,1,0,1,0,
%T -1,1,1,0,0,0,-1,-1,1,0,-1,0,-1,1,0,0,-1,0,0,-1,-1,0,-1,0,-1,-1,0,0,
%U -1,0,1,1,0,0,1,0,1,1,-1,0,1,0,1,1,1,0,1,0,-1,-1,1,0,0,0,-1,0,0,0,0,0,1,0,0,0,1,0,0,-1,1,0,0,0,-1,-1
%N a(n) = mu(A156552(n)), where mu is Möbius mu function.
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A008683(A156552(n)).
%F a(p) = 0 for primes p > 3.
%o (PARI)
%o A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
%o A342653(n) = moebius(A156552(n));
%Y Cf. A008683, A156552.
%Y Cf. also A323243, A324104, A324105, A324119, A342655 (sigma, phi, tau, omega and bigomega similarly permuted).
%K sign
%O 2
%A _Antti Karttunen_, Mar 18 2021