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A353422 Dirichlet convolution of A353350 with A353418 (the Dirichlet inverse of A353269). 4
1, 0, 0, -1, 0, 1, 0, 1, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, -1, -1, 0, -1, -1, 1, 1, 0, 0, -1, 0, -1, 1, -1, 1, 2, 0, 1, -1, 1, 0, 0, 0, 1, 0, -1, 0, 1, -1, 1, 1, 0, 0, -1, -1, -1, -1, 1, 0, -2, 0, -1, 1, 1, 1, -1, 0, 1, 1, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, -2, 0, -1, 0, 2, -1, 1, -1, 1, 0, 2, -1, 1, 1, -1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,36
COMMENTS
Dirichlet convolution between this sequence and A353362 is A353352.
LINKS
FORMULA
a(n) = Sum_{d|n} A353350(n/d) * A353418(d).
a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
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
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A353350(n) = (0==(A048675(n)%3));
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A353269(n) = (!(A156552(n)%3));
v353418 = DirInverseCorrect(vector(up_to, n, A353269(n)));
A353418(n) = v353418[n];
A353422(n) = sumdiv(n, d, A353350(n/d)*A353418(d));
CROSSREFS
Cf. A353421 (Dirichlet inverse).
Cf. also A353352, A353362.
Sequence in context: A359763 A277017 A178498 * A095408 A357375 A133008
KEYWORD
sign
AUTHOR
Antti Karttunen, Apr 19 2022
STATUS
approved

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Last modified May 19 13:04 EDT 2024. Contains 372692 sequences. (Running on oeis4.)