A349345 Sum of A109168 and its Dirichlet inverse, where A109168(n) = (n+A006519(n))/2, and A006519 is the highest power of 2 dividing n.

2, 0, 0, 4, 0, 8, 0, 8, 4, 12, 0, 8, 0, 16, 12, 16, 0, 12, 0, 12, 16, 24, 0, 16, 9, 28, 12, 16, 0, 8, 0, 32, 24, 36, 24, 20, 0, 40, 28, 24, 0, 12, 0, 24, 26, 48, 0, 32, 16, 34, 36, 28, 0, 32, 36, 32, 40, 60, 0, 32, 0, 64, 36, 64, 42, 20, 0, 36, 48, 24, 0, 40, 0, 76, 46, 40, 48, 24, 0, 48, 37, 84, 0, 44, 54, 88, 60, 48

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• nonn
• look

Links

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

Crossrefs

Cf. A109168, A349344.

Programs

PARI

up_to = 20000;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA109168(n) = ((n+bitand(n, -n))\2); \\ From A109168
v349344 = DirInverseCorrect(vector(up_to,n,A109168(n)));
A349344(n) = v349344[n];
A349345(n) = (A109168(n)+A349344(n));

Formula

a(n) = A109168(n) + A349344(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A109168(d) * A349344(n/d).

For all n >= 1, a(4*n) = 4*A109168(n). - Antti Karttunen, Dec 07 2021