cp's OEIS Frontend

A349368 Dirichlet inverse of A006369, the inverse permutation of "amusical permutation".

%I A349368 #9 Nov 25 2021 19:18:48
%S A349368 1,-3,-2,4,-7,8,-9,-8,-2,29,-15,-18,-17,35,18,16,-23,4,-25,-68,22,61,
%T A349368 -31,44,16,67,-2,-76,-39,-104,-41,-32,38,93,79,6,-49,99,42,168,-55,
%U A349368 -120,-57,-140,10,125,-63,-104,16,-128,58,-148,-71,0,137,184,62,157,-79,354,-81,163,14,64,151,-216,-89,-212,78,-445
%N A349368 Dirichlet inverse of A006369, the inverse permutation of "amusical permutation".
%H A349368 Antti Karttunen, <a href="/A349368/b349368.txt">Table of n, a(n) for n = 1..20000</a>
%F A349368 a(1) = 1; a(n) = -Sum_{d|n, d < n} A006369(n/d) * a(d).
%F A349368 a(n) = A349369(n) - A006369(n).
%o A349368 (PARI)
%o A349368 A006369(n) = if(!(n%3),(2/3)*n,(1/3)*if(1==(n%3),((4*n)-1),((4*n)+1)));
%o A349368 memoA349368 = Map();
%o A349368 A349368(n) = if(1==n,1,my(v); if(mapisdefined(memoA349368,n,&v), v, v = -sumdiv(n,d,if(d<n,A006369(n/d)*A349368(d),0)); mapput(memoA349368,n,v); (v)));
%Y A349368 Cf. A006369, A349369.
%Y A349368 Cf. also A349351, A349376.
%K A349368 sign
%O A349368 1,2
%A A349368 _Antti Karttunen_, Nov 17 2021