A349369 Sum of A006369 and its Dirichlet inverse, where A006369 is the inverse of "amusical permutation", A006368.

2, 0, 0, 9, 0, 12, 0, 3, 4, 42, 0, -10, 0, 54, 28, 37, 0, 16, 0, -41, 36, 90, 0, 60, 49, 102, 16, -39, 0, -84, 0, 11, 60, 138, 126, 30, 0, 150, 68, 221, 0, -92, 0, -81, 40, 186, 0, -72, 81, -61, 92, -79, 0, 36, 210, 259, 100, 234, 0, 394, 0, 246, 56, 149, 238, -172, 0, -121, 124, -352, 0, 8, 0, 294, -22, -119, 270

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, A349368.

Cf. also A349352, A349378.

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)));
A349369(n) = (A006369(n)+A349368(n));

Formula

a(n) = A006369(n) + A349368(n).

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1A006369(d) * A349368(n/d).