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A355685
Dirichlet inverse of A353380.
1
1, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, 1, 0, -1, 0, -1, 0, 0, 0, 2, -1, -1, -1, -1, 0, 0, 0, 1, -1, 0, -1, 2, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 3, -1, -1, -1, -1, 0, 2, 0, 2, 0, -1, 0, 1, 0, 0, -1, -1, -1, 0, 0, -1, -1, 0, 0, 5, 0, -1, -1, -1, -1, 0, 0, 2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, -1, -1, 0, -1, -2, 0, -1, -1, 1, 0, 0, 0, 2, 0
OFFSET
1,24
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A353380(n/d) * a(d).
a(p) = 0 for all primes p.
a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
PROG
(PARI)
A332823(n) = { my(f = factor(n), u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u, -1, u); };
A353354(n) = sumdiv(n, d, A332823(d));
A353380(n) = (0==A353354(n));
memoA355685 = Map();
A355685(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355685, n, &v), v, v = -sumdiv(n, d, if(d<n, A353380(n/d)*A355685(d), 0)); mapput(memoA355685, n, v); (v)));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 14 2022
STATUS
approved