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

1, -3, -2, 4, -7, 8, -9, -8, -2, 29, -15, -18, -17, 35, 18, 16, -23, 4, -25, -68, 22, 61, -31, 44, 16, 67, -2, -76, -39, -104, -41, -32, 38, 93, 79, 6, -49, 99, 42, 168, -55, -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

Offset: 1

Author

Antti Karttunen, Nov 17 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A006369, A349369.

Cf. also A349351, A349376.

Programs

PARI

A006369(n) = if(!(n%3),(2/3)*n,(1/3)*if(1==(n%3),((4*n)-1),((4*n)+1)));
memoA349368 = Map();
A349368(n) = if(1==n,1,my(v); if(mapisdefined(memoA349368,n,&v), v, v = -sumdiv(n,d,if(dA006369(n/d)*A349368(d),0)); mapput(memoA349368,n,v); (v)));

Formula

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

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