A353461 Dirichlet convolution of A003602 (Kimberling's paraphrases) with A323881 (the Dirichlet inverse of A126760).

1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 2, 0, 2, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 2, 0, 9, 0, 5, 0, 5, 0, 7, 0, 1, 0, 6, 0, 8, 0, 7, 0, 7, 0, 9, 0, 8, 0, 5, 0, 11, 0, 9, 0, 1, 0, 12, 0, 10, 0, 10, 0, 12, 0, 2, 0, 11, 0, 15, 0, 12, 0, 12, 0, 10, 0, 3, 0, 13, 0, 27, 0, 14, 0, 2, 0, 19, 0, 15, 0, 4, 0, 20, 0, 3, 0, 16, 0, 21

Offset: 1

Author

Antti Karttunen, Apr 20 2022

Keywords

• sign

Comments

Taking the Dirichlet convolution between this sequence and A349393 gives A349371, and similarly for many other such analogous pairs.

Links

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

Crossrefs

Cf. A003602, A126760, A323881, A353460 (Dirichlet inverse), A353462 (sum with it).

Cf. also A349371, A349393.

Programs

PARI

up_to = 65537;
A003602(n) = (1+(n>>valuation(n,2)))/2;
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(dA126760(n)));
A323881(n) = v323881[n];
A353461(n) = sumdiv(n,d,A003602(d)*A323881(n/d));

Formula

a(n) = Sum_{d|n} A003602(d) * A323881(n/d).

a(n) = A353462(n) - A353460(n).