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A353336
Sum of A353420 and its Dirichlet inverse.
5
2, 0, 0, 1, 0, 4, 0, 1, 4, 6, 0, 2, 0, 8, 12, 1, 0, 14, 0, 3, 16, 10, 0, 2, 9, 12, 28, 4, 0, 12, 0, 1, 20, 14, 24, 9, 0, 16, 24, 3, 0, 22, 0, 5, 66, 20, 0, 2, 16, 25, 28, 6, 0, 56, 30, 4, 32, 22, 0, 12, 0, 26, 100, 1, 36, 24, 0, 7, 40, 28, 0, 9, 0, 28, 86, 8, 40, 34, 0, 3, 157, 30, 0, 19, 42, 32, 44, 5, 0, 52, 48
OFFSET
1,1
COMMENTS
The first negative term is a(255255) = -11936.
FORMULA
a(n) = A353420(n) + A353335(n).
For n > 1, a(n) = -Sum_{d|n, 1<d<n} A353420(d) * A353335(n/d).
PROG
(PARI)
up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v (correctly!)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
v353335 = DirInverseCorrect(vector(up_to, n, A353420(n)));
A353335(n) = v353335[n];
A353336(n) = (A353420(n)+A353335(n));
CROSSREFS
Cf. A003961, A126760, A353420 (also a quadrisection of this sequence), A353335.
Cf. also A323882, A323894, A349135.
Sequence in context: A346236 A323365 A349135 * A349126 A340188 A323911
KEYWORD
sign
AUTHOR
Antti Karttunen, Apr 20 2022
STATUS
approved