A378453 Dirichlet inverse of A018892, where A018892(n) = (tau(n^2)+1)/2.

1, -2, -2, 1, -2, 3, -2, 0, 1, 3, -2, 0, -2, 3, 3, 0, -2, 0, -2, 0, 3, 3, -2, -1, 1, 3, 0, 0, -2, -2, -2, 0, 3, 3, 3, -2, -2, 3, 3, -1, -2, -2, -2, 0, 0, 3, -2, 0, 1, 0, 3, 0, -2, -1, 3, -1, 3, 3, -2, -3, -2, 3, 0, 0, 3, -2, -2, 0, 3, -2, -2, 0, -2, 3, 0, 0, 3, -2, -2, 0, 0, 3, -2, -3, 3, 3, 3, -1, -2, -3, 3, 0, 3, 3, 3

Offset

1,2

Comments

Möbius transform of A378452.

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} A018892(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A378452(d).

Prog

(PARI)
A018892(n) = ((numdiv(n^2)+1)/2);
memoA378453 = Map();
A378453(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378453, n, &v), v, v = -sumdiv(n, d, if(d<n, A018892(n/d)*A378453(d), 0)); mapput(memoA378453, n, v); (v)));

Crossrefs

Cf. A008683, A018892, A378452.

Sequence in context: A071694 A365393 A366286 * A378438 A072781 A340094

Adjacent sequences: A378450 A378451 A378452 * A378454 A378456 A378457

Keyword

sign,new

Author

Antti Karttunen, Nov 29 2024

Status

approved