A379106 - OEIS

%I #9 Dec 16 2024 22:18:59

%S 1,0,0,0,-2,2,-3,0,-3,2,-7,4,-9,2,2,0,-14,4,-15,4,-1,2,-18,8,-8,2,-4,

%T 4,-24,2,-25,0,-2,2,5,12,-33,2,0,8,-37,0,-38,4,10,2,-41,16,-20,0,2,4,

%U -48,2,15,8,0,2,-53,12,-55,2,19,0,16,-8,-63,4,-3,-4,-66,32,-69,2,-2,4,18,-12,-73,16,-15,2,-78,8,30

%N Dirichlet convolution of A000120 and A323910, where A323910 is the Dirichlet inverse of the deficiency of n, and A000120 is the binary weight of n.

%H Antti Karttunen, <a href="/A379106/b379106.txt">Table of n, a(n) for n = 1..20000</a>

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

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

%F a(n) = Sum_{d|n} A000120(d)*A323910(n/d).

%o (PARI)

%o A033879(n) = (n+n-sigma(n));

%o memoA323910 = Map();

%o A323910(n) = if(1==n,1,my(v); if(mapisdefined(memoA323910,n,&v), v, v = -sumdiv(n,d,if(d<n,A033879(n/d)*A323910(d),0)); mapput(memoA323910,n,v); (v)));

%o A379106(n) = sumdiv(n,d,hammingweight(d)*A323910(n/d));

%Y Cf. A000120, A033879, A323910, A379107 (Dirichlet inverse).

%Y Cf. also A294898, A378754, A378756.

%K sign,new

%O 1,5

%A _Antti Karttunen_, Dec 16 2024