A378224 Dirichlet inverse of A378223.

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

Offset

1,3

Comments

Möbius transform of A378218.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A378223(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A378218(d).

Prog

(PARI)
memoA345182 = Map();
A345182(n) = if(n<=2, n%2, my(v); if(mapisdefined(memoA345182, n, &v), v, v = sumdiv(n, d, if(d<n, A345182(d), 0)); mapput(memoA345182, n, v); (v)));
A378223(n) = sumdiv(n, d, A345182(d));
memoA378224 = Map();
A378224(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378224, n, &v), v, v = -sumdiv(n, d, if(d<n, A378223(n/d)*A378224(d), 0)); mapput(memoA378224, n, v); (v)));

Crossrefs

Cf. A008683, A345182, A378218, A378223.

Cf. also A378225.

Sequence in context: A046920 A107599 A156836 * A287438 A079483 A262115

Adjacent sequences: A378221 A378222 A378223 * A378225 A378226 A378227

Keyword

sign

Author

Antti Karttunen, Nov 25 2024

Status

approved