A353468 Dirichlet inverse of A353467.

1, 1, -1, -1, 1, 1, -1, 2, 2, -1, 1, -3, -1, 1, -3, -5, 1, -1, -1, 3, 3, -1, 1, 10, -1, 1, -5, -3, -1, 1, 1, 14, -3, -1, 1, 0, -1, 1, 3, -10, 1, -1, -1, 3, 10, -1, 1, -35, 2, 2, -3, -3, -1, 2, -1, 10, 3, 1, 1, 3, -1, -1, -10, -42, 1, 1, 1, 3, -3, -3, -1, 10, 1, 1, 0, -3, -3, -1, -1, 35, 14, -1, 1, -3, -1, 1, 3, -10

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

a(1) = 1, for n > 1, a(n) = -Sum_{d|n, d<n} A353467(n/d) * a(d).

a(n) = A353467(A252463(n)).

For all n >= 1, a(A000040(n)) = ((-1)^(n-1)).

Prog

(PARI)
A252463(n) = if(!(n%2), n/2, my(f=factor(n)); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f));
memoA353467 = Map();
A353467(n) = if(1==n, 1, my(v); if(mapisdefined(memoA353467, n, &v), v, v = -sumdiv(n, d, if(d<n, A353467(A252463(n/d))*A353467(d), 0)); mapput(memoA353467, n, v); (v)));
A353468(n) = A353467(A252463(n));

Crossrefs

Cf. A000040, A252463, A353467 [Dirichlet inverse], A353469 [sum with it].

Cf. also A353458.

Sequence in context: A318810 A319989 A338117 * A184305 A337279 A157522

Adjacent sequences: A353465 A353466 A353467 * A353469 A353470 A353471

Keyword

sign

Author

Antti Karttunen, Apr 21 2022

Status

approved