A353461 -id:A353461 - cp's OEIS frontend

A353462 a(n) = A353460(n) + A353461(n).

2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 9, 0, 0, 0, 1, 0, 6, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 11, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 7, 0, 4, 0, 0, 0, 19, 0, 0, 0, 6, 0, 10, 0, 0, 0, 4, 0, 10, 0, 6, 0, 0, 0, 20, 0, 0, 0, 0, 0, 10

Offset: 1

Antti Karttunen, Apr 20 2022

sign

The first negative term is a(935) = -8.

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

Cf. A353460, A353461.

PARI
```
A353462(n) = (A353460(n) + A353461(n));
```

a(n) = A353460(n) + A353461(n).

For n > 1, a(n) = -Sum_{d|n, 1A353460(d) * A353461(n/d). [As the sequences are Dirichlet inverses of each other]

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

Original entry on oeis.org

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

Antti Karttunen, Apr 20 2022

sign

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

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

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

Cf. also A349371, A349380, A349393, A349432.

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));

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

cp's OEIS Frontend

A353462 a(n) = A353460(n) + A353461(n).

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