cp's OEIS Frontend

A297115 Möbius transform of A000120, binary weight of n.

%I A297115 #8 Dec 26 2017 21:25:02
%S A297115 1,0,1,0,1,0,2,0,0,0,2,0,2,0,1,0,1,0,2,0,-1,0,3,0,1,0,2,0,3,0,4,0,-2,
%T A297115 0,-1,0,2,0,0,0,2,0,3,0,0,0,4,0,0,0,1,0,3,0,1,0,0,0,4,0,4,0,3,0,-2,0,
%U A297115 2,0,-2,0,3,0,2,0,-1,0,-1,0,4,0,-1,0,3,0,1,0,0,0,3,0,0,0,-1,0,2,0,2,0,2,0,3,0,4,0,0
%N A297115 Möbius transform of A000120, binary weight of n.
%H A297115 Antti Karttunen, <a href="/A297115/b297115.txt">Table of n, a(n) for n = 1..16384</a>
%H A297115 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A297115 a(n) = Sum_{d|n} A008683(n/d)*A000120(d).
%F A297115 a(n) = A083254(n) - A297114(n).
%F A297115 a(2n) = 0.
%o A297115 (PARI) A297115(n) = sumdiv(n,d,moebius(n/d)*hammingweight(d));
%Y A297115 Cf. A000120, A008683, A083254, A297114, A297116 (odd bisection), A297117.
%K A297115 sign
%O A297115 1,7
%A A297115 _Antti Karttunen_, Dec 26 2017