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A354187
Sum of A348717 and its Dirichlet inverse.
3
2, 0, 0, 4, 0, 8, 0, 8, 4, 8, 0, 16, 0, 8, 8, 16, 0, 16, 0, 32, 8, 8, 0, 24, 4, 8, 8, 48, 0, 40, 0, 32, 8, 8, 8, 44, 0, 8, 8, 40, 0, 72, 0, 80, 16, 8, 0, 48, 4, 32, 8, 96, 0, 48, 8, 56, 8, 8, 0, 56, 0, 8, 32, 64, 8, 120, 0, 128, 8, 72, 0, 64, 0, 8, 16, 144, 8, 168, 0, 80, 16, 8, 0, 72, 8, 8, 8, 88, 0, 80, 8, 176
OFFSET
1,1
COMMENTS
The first negative term is a(520) = -8.
FORMULA
a(n) = A348717(n) + A354186(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A348717(d) * A354186(n/d).
PROG
(PARI)
A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
memoA354186 = Map();
A354186(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354186, n, &v), v, v = -sumdiv(n, d, if(d<n, A348717(n/d)*A354186(d), 0)); mapput(memoA354186, n, v); (v)));
A354187(n) = (A348717(n)+A354186(n));
CROSSREFS
Sequence in context: A353369 A323900 A349347 * A349345 A349357 A071390
KEYWORD
sign
AUTHOR
Antti Karttunen, May 19 2022
STATUS
approved