A378225 Dirichlet inverse of A067824.

1, -2, -2, 0, -2, 2, -2, 0, 0, 2, -2, 0, -2, 2, 2, 0, -2, 0, -2, 0, 2, 2, -2, 0, 0, 2, 0, 0, -2, -2, -2, 0, 2, 2, 2, 0, -2, 2, 2, 0, -2, -2, -2, 0, 0, 2, -2, 0, 0, 0, 2, 0, -2, 0, 2, 0, 2, 2, -2, 0, -2, 2, 0, 0, 2, -2, -2, 0, 2, -2, -2, 0, -2, 2, 0, 0, 2, -2, -2, 0, 0, 2, -2, 0, 2, 2, 2, 0, -2, 0, 2, 0, 2, 2, 2, 0, -2

Offset

1,2

Comments

Möbius transform of A153881.

Links

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

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A067824(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A153881(d).

Dirichlet g.f.: (2 - zeta(s)) / zeta(s). [See Dec 30 2018 formula in A067824]

Prog

(PARI)
A074206(n) = if(n>1, sumdiv(n, i, if(i<n, A074206(i))), n); \\ From A074206
A067824(n) = sumdiv(n, d, A074206(d));
memoA378225 = Map();
A378225(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378225, n, &v), v, v = -sumdiv(n, d, if(d<n, A067824(n/d)*A378225(d), 0)); mapput(memoA378225, n, v); (v)));

Crossrefs

Cf. A008683, A067824, A153881.

Cf. also A378224.

Sequence in context: A029310 A348220 A134131 * A354186 A366265 A127527

Adjacent sequences: A378222 A378223 A378224 * A378226 A378227 A378228

Keyword

sign

Author

Antti Karttunen, Nov 25 2024

Status

approved