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A364571 a(n) = A297171(A163511(n)), where A297171 is the Möbius transform of the inverse permutation of A163511.

%I A364571 #14 Aug 06 2023 08:19:53
%S A364571 0,1,1,3,2,2,2,7,4,4,2,4,5,3,6,15,8,8,4,8,4,4,4,8,10,10,4,5,13,11,14,
%T A364571 31,16,16,8,16,8,8,8,16,8,8,4,8,8,8,8,16,20,20,10,20,7,9,6,9,26,26,12,
%U A364571 21,29,27,30,63,32,32,16,32,16,16,16,32,16,16,8,16,16,16,16,32,16,16,8,16,8,8,8,16,16,16
%N A364571 a(n) = A297171(A163511(n)), where A297171 is the Möbius transform of the inverse permutation of A163511.
%H A364571 Antti Karttunen, <a href="/A364571/b364571.txt">Table of n, a(n) for n = 0..16383</a>
%H A364571 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A364571 a(n) = A297171(A163511(n)).
%o A364571 (PARI)
%o A364571 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A364571 A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
%o A364571 A163511(n) = if(!n,1,A005940(1+A054429(n)));
%o A364571 A243071(n) = if(n<=2, n-1, 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]); ((3<<#binary(res\2))-res-1)); \\ (Combining programs given in A156552 and A054429) - _Antti Karttunen_, Aug 05 2023
%o A364571 A297171(n) = sumdiv(n,d,moebius(n/d)*A243071(d));
%o A364571 A364571(n) = A297171(A163511(n));
%Y A364571 Cf. A163511, A243071, A297171.
%Y A364571 Cf. also A364567.
%K A364571 nonn,look
%O A364571 0,4
%A A364571 _Antti Karttunen_, Aug 05 2023