A349453 - OEIS

%I #16 Feb 24 2022 09:03:31

%S 1,-3,-9,-18,-81,-189,-729,-2052,-6480,-19197,-59049,-175446,-531441,

%T -1589949,-4781511,-14335704,-43046721,-129097152,-387420489,

%U -1162141182,-3486771279,-10459998909,-31381059609,-94142073420,-282429529920,-847285420797,-2541865710960,-7625587899366,-22876792454961,-68630348286531

%N Dirichlet inverse of A133494, 3^(n-1).

%H Antti Karttunen, <a href="/A349453/b349453.txt">Table of n, a(n) for n = 1..1001</a>

%F a(1) = 1; a(n) = -Sum_{d|n, d < n} A133494(n/d) * a(d).

%F G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} 3^(k-1) * A(x^k). - _Ilya Gutkovskiy_, Feb 23 2022

%t a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#] * 3^(n/# - 1) &, # < n &]; Array[a, 30] (* _Amiram Eldar_, Nov 22 2021 *)

%o (PARI)

%o A133494(n) = max(1, 3^(n-1));

%o memoA349453 = Map();

%o A349453(n) = if(1==n,1,my(v); if(mapisdefined(memoA349453,n,&v), v, v = -sumdiv(n,d,if(d<n,A133494(n/d)*A349453(d),0)); mapput(memoA349453,n,v); (v)));

%Y Cf. A133494.

%Y Cf. also A349449, A349450, A349451, A349452, A349568.

%K sign

%O 1,2

%A _Antti Karttunen_, Nov 22 2021