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

1,4

Comments

Inverse Möbius transform of A378534.

Links

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

Formula

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

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

Prog

(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(d<n, A378542(n/d)*A378525(d), 0)); mapput(memoA378525, n, v); (v)));
A378532(n) = sumdiv(n, d, A296075(d)*A378525(n/d));

Crossrefs

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

Cf. also A378218.

Sequence in context: A325799 A355930 A229946 * A378531 A127460 A274021

Adjacent sequences: A378529 A378530 A378531 * A378533 A378534 A378535

Keyword

sign,new

Author

Antti Karttunen, Dec 01 2024

Status

approved