A346479 Dirichlet inverse of A250469.

1, -3, -5, 0, -7, 15, -11, 6, 0, 15, -13, 12, -17, 27, 35, 0, -19, 24, -23, 42, 55, 15, -29, -66, 0, 27, 60, 54, -31, -27, -37, -12, 45, 15, 77, -144, -41, 27, 75, -102, -43, -63, -47, 132, 60, 39, -53, -24, 0, 84, 65, 144, -59, -384, 91, -162, 85, 15, -61, -558, -67, 39, 120, 0, 119, 165, -71, 222, 115, 9, -73, 168

Offset

1,2

Comments

Not all zeros occur on squares. For example, a(1445) = a(5 * 17^2) = 0.

Links

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

Index entries for sequences generated by sieves

Formula

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

a(n) = A346480(n) - A250469(n).

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];

Crossrefs

Cf. A250469, A346480.

Cf. also A346234, A346477.

Sequence in context: A222480 A229984 A346234 * A346254 A021289 A200480

Adjacent sequences: A346476 A346477 A346478 * A346480 A346481 A346482

Keyword

sign

Author

Antti Karttunen, Jul 30 2021

Status

approved