A323882 Sum of A126760 and its Dirichlet inverse.

2, 0, 0, 1, 0, 2, 0, 1, 1, 4, 0, 1, 0, 6, 4, 1, 0, 1, 0, 2, 6, 8, 0, 1, 4, 10, 1, 3, 0, 0, 0, 1, 8, 12, 12, 1, 0, 14, 10, 2, 0, 0, 0, 4, 2, 16, 0, 1, 9, 14, 12, 5, 0, 1, 16, 3, 14, 20, 0, 2, 0, 22, 3, 1, 20, 0, 0, 6, 16, 12, 0, 1, 0, 26, 14, 7, 24, 0, 0, 2, 1, 28, 0, 3, 24, 30, 20, 4, 0, 2, 30, 8, 22, 32, 28, 1, 0, 25, 4, 9, 0, 0, 0, 5, 12

Offset

1,1

Comments

From Antti Karttunen, Aug 18 2021: (Start)

No negative terms in range 1 .. 2^20.

Apparently zeros occur only on (some of the) positions given by A030059, with exceptions for example on n = 70, 105, 110, 130, 154, etc, where a(n) > 0.

(End)

Links

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

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = A126760(n) + A323881(n).

For n > 1, a(n) = -Sum_{d|n, 1<d<n} A126760(d) * A323881(n/d). - Antti Karttunen, Aug 18 2021

Prog

(PARI)
up_to = 20000;
A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v
v323881 = DirInverseCorrect(vector(up_to, n, A126760(n)));
A323881(n) = v323881[n];
A323882(n) = (A126760(n)+A323881(n));

Crossrefs

Cf. A030059, A126760, A323881, A323884, A323885, A323887.

Sequence in context: A307377 A353367 A349439 * A349446 A353469 A349433

Adjacent sequences: A323879 A323880 A323881 * A323883 A323884 A323885

Keyword

nonn,look

Author

Antti Karttunen, Feb 08 2019

Status

approved