A378533 Dirichlet convolution of A323910 and A378542.

1, 1, 1, 3, 1, 4, 1, 5, 3, 4, 1, 10, 1, 4, 4, 11, 1, 10, 1, 10, 4, 4, 1, 26, 3, 4, 5, 10, 1, 16, 1, 21, 4, 4, 4, 34, 1, 4, 4, 26, 1, 16, 1, 10, 10, 4, 1, 62, 3, 10, 4, 10, 1, 26, 4, 26, 4, 4, 1, 56, 1, 4, 10, 43, 4, 16, 1, 10, 4, 16, 1, 98, 1, 4, 10, 10, 4, 16, 1, 62, 11, 4, 1, 56, 4, 4, 4, 26, 1, 56, 4, 10, 4, 4, 4

Offset

1,4

Comments

Inverse Möbius transform of A378531.

Links

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

Formula

a(n) = Sum_{d|n} A323910(d)*A378542(n/d).

a(n) = Sum_{d|n} A378531(d).

Prog

(PARI)
A378542(n) = sumdiv(n, d, d*!(bigomega(n/d)%2));
A033879(n) = (n+n-sigma(n));
memoA323910 = Map();
A323910(n) = if(1==n, 1, my(v); if(mapisdefined(memoA323910, n, &v), v, v = -sumdiv(n, d, if(d<n, A033879(n/d)*A323910(d), 0)); mapput(memoA323910, n, v); (v)));
A378533(n) = sumdiv(n, d, A323910(d)*A378542(n/d));

Crossrefs

Cf. A323910, A378542.

Cf. A378531 (Möbius transform), A378534 (Dirichlet inverse).

Cf. also A378223.

Sequence in context: A166050 A259655 A221185 * A242746 A363258 A327642

Adjacent sequences: A378530 A378531 A378532 * A378534 A378535 A378536

Keyword

nonn

Author

Antti Karttunen, Dec 01 2024

Status

approved