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

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Comments

Inverse Möbius transform of A378531.

Links

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

Crossrefs

Cf. A323910, A378542.

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

Cf. also A378223.

Programs

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(dA033879(n/d)*A323910(d),0)); mapput(memoA323910,n,v); (v)));
A378533(n) = sumdiv(n,d,A323910(d)*A378542(n/d));

Formula

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

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