A378532 Dirichlet convolution of A296075 and A378525.

1, 0, 0, -2, 0, -3, 0, -2, -2, -3, 0, -4, 0, -3, -3, -2, 0, -4, 0, -4, -3, -3, 0, -2, -2, -3, -2, -4, 0, -6, 0, -2, -3, -3, -3, -1, 0, -3, -3, -2, 0, -6, 0, -4, -4, -3, 0, -2, -2, -4, -3, -4, 0, -2, -3, -2, -3, -3, 0, 0, 0, -3, -4, -2, -3, -6, 0, -4, -3, -6, 0, 0, 0, -3, -4, -4, -3, -6, 0, -2, -2, -3, 0, 0, -3, -3, -3, -2

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• sign

Comments

Inverse Möbius transform of A378534.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A033879, A296075, A378531 (Dirichlet inverse), A378534 (Möbius transform), A378525, A378542.

Cf. also A378218.

Programs

PARI

A033879(n) = ((2*n)-sigma(n));
A296075(n) = sumdiv(n,d,A033879(d));
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)));
A378532(n) = sumdiv(n,d,A296075(d)*A378525(n/d));

Formula

a(n) = Sum_{d|n} A296075(d)*A378525(n/d).

a(n) = Sum_{d|n} A378534(d).