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Dirichlet inverse of A006369, the inverse permutation of "amusical permutation".
4

%I #9 Nov 25 2021 19:18:48

%S 1,-3,-2,4,-7,8,-9,-8,-2,29,-15,-18,-17,35,18,16,-23,4,-25,-68,22,61,

%T -31,44,16,67,-2,-76,-39,-104,-41,-32,38,93,79,6,-49,99,42,168,-55,

%U -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 Dirichlet inverse of A006369, the inverse permutation of "amusical permutation".

%H Antti Karttunen, <a href="/A349368/b349368.txt">Table of n, a(n) for n = 1..20000</a>

%F a(1) = 1; a(n) = -Sum_{d|n, d < n} A006369(n/d) * a(d).

%F a(n) = A349369(n) - A006369(n).

%o (PARI)

%o A006369(n) = if(!(n%3),(2/3)*n,(1/3)*if(1==(n%3),((4*n)-1),((4*n)+1)));

%o memoA349368 = Map();

%o 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 Cf. A006369, A349369.

%Y Cf. also A349351, A349376.

%K sign

%O 1,2

%A _Antti Karttunen_, Nov 17 2021