A378452 Dirichlet inverse of A007875, where A007875(n) = phi(2^omega(n)).

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

Offset

1,30

Comments

Inverse Möbius transform of A378453.

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} A007875(n/d) * a(d).

a(n) = Sum_{d|n} A378453(d).

Prog

(PARI)
A007875(n) = eulerphi(2^omega(n));
memoA378452 = Map();
A378452(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378452, n, &v), v, v = -sumdiv(n, d, if(d<n, A007875(n/d)*A378452(d), 0)); mapput(memoA378452, n, v); (v)));

Crossrefs

Cf. A007875, A378453 (Möbius transform).

Sequence in context: A263774 A161519 A286561 * A068101 A094263 A049761

Adjacent sequences: A378449 A378450 A378451 * A378453 A378454 A378456

Keyword

sign,new

Author

Antti Karttunen, Nov 29 2024

Status

approved