A378534 Dirichlet convolution of A033879 and A378525.

1, -1, -1, -2, -1, -2, -1, 0, -2, -2, -1, 1, -1, -2, -2, 0, -1, 1, -1, 1, -2, -2, -1, 2, -2, -2, 0, 1, -1, 2, -1, 0, -2, -2, -2, 4, -1, -2, -2, 2, -1, 2, -1, 1, 1, -2, -1, 0, -2, 1, -2, 1, -1, 2, -2, 2, -2, -2, -1, 6, -1, -2, 1, 0, -2, 2, -1, 1, -2, 2, -1, -1, -1, -2, 1, 1, -2, 2, -1, 0, 0, -2, -1, 6, -2, -2, -2, 2, -1, 6

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• sign

Comments

Möbius transform of A378532.

Links

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

Crossrefs

Cf. A008683, A033879, A323910, A378532 (inverse Möbius transform), A378533 (Dirichlet inverse), A378542.

Cf. also A378224.

Programs

PARI

A033879(n) = (n+n-sigma(n));
A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
memoA378525 = Map();
A378525(n) = if(1==n,1,my(v); if(mapisdefined(memoA378525,n,&v), v, v = -sumdiv(n,d,if(dA378542(n/d)*A378525(d),0)); mapput(memoA378525,n,v); (v)));
A378534(n) = sumdiv(n,d,A033879(d)*A378525(n/d));

Formula

a(n) = Sum_{d|n} A033879(d)*A378525(n/d).

a(n) = Sum_{d|n} A008683(d)*A378532(n/d).