A324730 - OEIS

%I #6 Mar 17 2019 21:07:36

%S 0,0,0,1,0,-1,0,1,2,0,0,2,0,1,1,-1,0,0,0,1,0,2,0,0,1,1,0,2,0,3,0,2,-1,

%T 2,-1,1,0,5,2,-2,0,-1,0,2,2,4,0,1,0,-3,-5,3,0,-3,-2,2,4,1,0,0,0,2,-2,

%U -1,-3,4,0,1,3,0,0,2,0,7,0,4,-1,4,0,2,0,2,0,1,0,7,2,0,0,2,2,3,1,4,1,-1,0,-2,2,2,0,1,0,0,2

%N Difference between the binary weight of A323243 and the binary weight of its Xor Moebius transform (negated).

%H Antti Karttunen, <a href="/A324730/b324730.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A324829(n) - A324729(n).

%F a(p) = 0 for all primes p.

%o (PARI)

%o A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v,

%o A323243(d)))); (v); }; \\ Needs also code from A323243.

%o A324729(n) = hammingweight(A323243(n)); \\ Needs also code from A323243.

%o A324829(n) = hammingweight(A324712(n));

%o A324730(n) = (A324829(n) - A324729(n));

%Y Cf. A000120, A323243, A324712, A324729, A324829.

%K sign

%O 1,9

%A _Antti Karttunen_, Mar 17 2019