cp's OEIS Frontend

A378991 Dirichlet inverse of the Möbius transform of A005187, where A005187(n) = 2*n - (number of 1's in binary representation of n).

%I A378991 #7 Dec 15 2024 09:30:36
%S A378991 1,-2,-3,0,-7,8,-10,0,-3,20,-18,-4,-22,28,27,0,-31,6,-34,-12,35,52,
%T A378991 -41,0,10,64,11,-16,-53,-104,-56,0,66,92,91,4,-70,100,84,0,-78,-132,
%U A378991 -81,-32,21,120,-88,0,16,-66,123,-40,-101,-56,173,0,132,156,-112,124,-116,164,51,0,210,-256,-130,-60,156,-364,-137
%N A378991 Dirichlet inverse of the Möbius transform of A005187, where A005187(n) = 2*n - (number of 1's in binary representation of n).
%H A378991 Antti Karttunen, <a href="/A378991/b378991.txt">Table of n, a(n) for n = 1..20020</a>
%F A378991 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A297111(n/d) * a(d).
%F A378991 a(n) = Sum_{d|n} A346237(d).
%o A378991 (PARI)
%o A378991 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A378991 A297111(n) = sumdiv(n,d,moebius(n/d)*A005187(d));
%o A378991 memoA378991 = Map();
%o A378991 A378991(n) = if(1==n,1,my(v); if(mapisdefined(memoA378991,n,&v), v, v = -sumdiv(n,d,if(d<n,A297111(n/d)*A378991(d),0)); mapput(memoA378991,n,v); (v)));
%Y A378991 Dirichlet inverse of A297111.
%Y A378991 Inverse Möbius transform of A346237.
%Y A378991 Cf. A005187.
%Y A378991 Cf. also A378989, A378990.
%K A378991 sign
%O A378991 1,2
%A A378991 _Antti Karttunen_, Dec 15 2024