A353460 Dirichlet convolution of A126760 with A349134 (the Dirichlet inverse of Kimberling's paraphrases).

1, 0, -1, 0, -1, 0, -1, 0, -2, 0, -2, 0, -2, 0, -1, 0, -3, 0, -3, 0, -2, 0, -4, 0, -1, 0, -4, 0, -5, 0, -5, 0, -3, 0, 1, 0, -6, 0, -4, 0, -7, 0, -7, 0, 0, 0, -8, 0, -4, 0, -5, 0, -9, 0, 3, 0, -6, 0, -10, 0, -10, 0, -1, 0, 2, 0, -11, 0, -7, 0, -12, 0, -12, 0, -3, 0, 1, 0, -13, 0, -8, 0, -14, 0, 4, 0, -9, 0, -15, 0, 0, 0

Offset: 1

Author

Antti Karttunen, Apr 20 2022

Keywords

• sign

Comments

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

Links

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

Crossrefs

Cf. A003602, A126760, A349134, A353461 (Dirichlet inverse), A353462 (sum with it).

Cf. also A349371, A349380, A349393, A349432.

Programs

PARI

A003602(n) = (1+(n>>valuation(n,2)))/2;
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
memoA349134 = Map();
A349134(n) = if(1==n,1,my(v); if(mapisdefined(memoA349134,n,&v), v, v = -sumdiv(n,d,if(dA003602(n/d)*A349134(d),0)); mapput(memoA349134,n,v); (v)));
A353460(n) = sumdiv(n,d,A126760(d)*A349134(n/d));

Formula

a(n) = Sum_{d|n} A126760(d) * A349134(n/d).