cp's OEIS Frontend

A349452 Dirichlet inverse of A011782, 2^(n-1).

%I A349452 #16 Feb 24 2022 09:02:15
%S A349452 1,-2,-4,-4,-16,-16,-64,-104,-240,-448,-1024,-1904,-4096,-7936,-16256,
%T A349452 -32272,-65536,-129888,-262144,-522176,-1048064,-2093056,-4194304,
%U A349452 -8379520,-16776960,-33538048,-67106880,-134184704,-268435456,-536801024,-1073741824,-2147352224,-4294959104,-8589672448,-17179867136,-34359197184
%N A349452 Dirichlet inverse of A011782, 2^(n-1).
%H A349452 Antti Karttunen, <a href="/A349452/b349452.txt">Table of n, a(n) for n = 1..1001</a>
%F A349452 a(1) = 1; a(n) = -Sum_{d|n, d < n} A011782(n/d) * a(d).
%F A349452 G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} 2^(k-1) * A(x^k). - _Ilya Gutkovskiy_, Feb 23 2022
%t A349452 a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#] * 2^(n/# - 1) &, # < n &]; Array[a, 36] (* _Amiram Eldar_, Nov 22 2021 *)
%o A349452 (PARI)
%o A349452 A011782(n) = (2^(n-1));
%o A349452 memoA349452 = Map();
%o A349452 A349452(n) = if(1==n,1,my(v); if(mapisdefined(memoA349452,n,&v), v, v = -sumdiv(n,d,if(d<n,A011782(n/d)*A349452(d),0)); mapput(memoA349452,n,v); (v)));
%Y A349452 Cf. A011782.
%Y A349452 Cf. also A349449, A349450, A349451, A349453 and A349563, A349565, A349567, A349569.
%K A349452 sign
%O A349452 1,2
%A A349452 _Antti Karttunen_, Nov 22 2021