A378531 Dirichlet convolution of A378432 and A378542.

1, 0, 0, 2, 0, 3, 0, 2, 2, 3, 0, 4, 0, 3, 3, 6, 0, 4, 0, 4, 3, 3, 0, 14, 2, 3, 2, 4, 0, 6, 0, 10, 3, 3, 3, 18, 0, 3, 3, 14, 0, 6, 0, 4, 4, 3, 0, 30, 2, 4, 3, 4, 0, 14, 3, 14, 3, 3, 0, 30, 0, 3, 4, 22, 3, 6, 0, 4, 3, 6, 0, 48, 0, 3, 4, 4, 3, 6, 0, 30, 6, 3, 0, 30, 3, 3, 3, 14, 0, 30, 3, 4, 3, 3, 3, 74, 0, 4, 4, 18

Offset

1,4

Comments

Möbius transform of A378533.

Links

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

Formula

a(n) = Sum_{d|n} A378432(d)*A378542(n/d).

a(n) = Sum_{d|n} A008683(d)*A378533(n/d).

Prog

(PARI)
A033879(n) = ((2*n)-sigma(n));
A296075(n) = sumdiv(n, d, A033879(d));
memoA378432 = Map();
A378432(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378432, n, &v), v, v = -sumdiv(n, d, if(d<n, A296075(n/d)*A378432(d), 0)); mapput(memoA378432, n, v); (v)));
A378542(n) = sumdiv(n, d, d*!(bigomega(n/d)%2));
A378531(n) = sumdiv(n, d, A378432(d)*A378542(n/d));

Crossrefs

Cf. A008683, A378532 (Dirichlet inverse), A378432, A378533 (inverse Möbius transform), A378542.

Cf. also A345182.

Sequence in context: A355930 A229946 A378532 * A127460 A274021 A303711

Adjacent sequences: A378528 A378529 A378530 * A378532 A378533 A378534

Keyword

nonn

Author

Antti Karttunen, Dec 01 2024

Status

approved