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

1,9

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

Formula

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

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

Prog

(PARI)
up_to = 65537;
A003602(n) = (1+(n>>valuation(n, 2)))/2;
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];
A353461(n) = sumdiv(n, d, A003602(d)*A323881(n/d));

Crossrefs

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

Cf. also A349371, A349393.

Sequence in context: A118514 A190544 A172293 * A161970 A230446 A260737

Adjacent sequences: A353458 A353459 A353460 * A353462 A353463 A353464

Keyword

sign

Author

Antti Karttunen, Apr 20 2022

Status

approved