A346480 Sum of A250469 and its Dirichlet inverse.

2, 0, 0, 9, 0, 30, 0, 27, 25, 42, 0, 45, 0, 66, 70, 45, 0, 75, 0, 99, 110, 78, 0, 3, 49, 102, 125, 135, 0, 60, 0, 81, 130, 114, 154, -39, 0, 138, 170, 15, 0, 60, 0, 261, 175, 174, 0, 117, 121, 231, 190, 297, 0, -225, 182, 3, 230, 186, 0, -381, 0, 222, 275, 189, 238, 360, 0, 423, 290, 216, 0, 381, 0, 246, 245, 459

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences generated by sieves

Formula

a(n) = A250469(n) + A346479(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A250469(d) * A346479(n/d).

Prog

(PARI)
up_to = 16384;
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.
v346479 = DirInverseCorrect(vector(up_to, n, A250469(n)));
A346479(n) = v346479[n];
A346480(n) = (A250469(n)+A346479(n));
(PARI) A346480(n) = if(1==n, 2, -sumdiv(n, d, if((1==d)||n==d, 0, A250469(d)*A346479(n/d)))); \\ (Demonstrates the convolution formula).

Crossrefs

Cf. A250469, A346479.

Cf. also A346478.

Sequence in context: A347229 A347095 A346255 * A323399 A246714 A246708

Adjacent sequences: A346477 A346478 A346479 * A346481 A346482 A346483

Keyword

sign

Author

Antti Karttunen, Jul 30 2021

Status

approved