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A378225
Dirichlet inverse of A067824.
3
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
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. also A378224.
Sequence in context: A029310 A348220 A134131 * A354186 A366265 A127527
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 25 2024
STATUS
approved