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A324878 Xor-Moebius transform of A324398, where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).

%I A324878 #10 Mar 19 2019 23:01:30
%S A324878 0,0,0,1,0,1,0,0,6,0,0,1,0,1,8,8,0,6,0,0,16,1,0,0,0,1,12,1,0,8,0,8,0,
%T A324878 1,20,8,0,1,66,0,0,17,0,1,8,1,0,8,0,0,2,1,0,12,36,0,258,1,0,0,0,1,16,
%U A324878 40,0,1,0,1,0,20,0,24,0,1,24,1,32,67,0,8,0,1,0,1,132,1,1026,0,0,40,72,1,0,1,256,16,0,1,68,16,0,3,0,0,46
%N A324878 Xor-Moebius transform of A324398, where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).
%H A324878 Antti Karttunen, <a href="/A324878/b324878.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A324878 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324878 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324878 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324878 a(p) = 0 for all primes p.
%o A324878 (PARI)
%o A324878 A156552(n) = {my(f = factor(n), 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}; \\ From A156552
%o A324878 A318458(n) = bitand(n, sigma(n)-n);
%o A324878 A324398(n) = if(1==n,0,A318458(A156552(n)));
%o A324878 \\ Or, equivalently:
%o A324878 A324398(n) = { my(k=A156552(n)); bitand(k,(A323243(n)-k)); }; \\ Needs also code from A323243.
%o A324878 A324878(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324398(d)))); (v); };
%Y A324878 Cf. A156552, A318458, A324820, A324821, A324876, A324877.
%K A324878 nonn
%O A324878 1,9
%A A324878 _Antti Karttunen_, Mar 18 2019