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A353461
Dirichlet convolution of A003602 (Kimberling's paraphrases) with A323881 (the Dirichlet inverse of A126760).
3
1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 2, 0, 2, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 2, 0, 9, 0, 5, 0, 5, 0, 7, 0, 1, 0, 6, 0, 8, 0, 7, 0, 7, 0, 9, 0, 8, 0, 5, 0, 11, 0, 9, 0, 1, 0, 12, 0, 10, 0, 10, 0, 12, 0, 2, 0, 11, 0, 15, 0, 12, 0, 12, 0, 10, 0, 3, 0, 13, 0, 27, 0, 14, 0, 2, 0, 19, 0, 15, 0, 4, 0, 20, 0, 3, 0, 16, 0, 21
OFFSET
1,9
COMMENTS
Taking the Dirichlet convolution between this sequence and A349393 gives A349371, and similarly for many other such analogous pairs.
LINKS
FORMULA
a(n) = Sum_{d|n} A003602(d) * A323881(n/d).
a(n) = A353462(n) - A353460(n).
PROG
(PARI)
up_to = 65537;
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
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
v323881 = DirInverseCorrect(vector(up_to, n, A126760(n)));
A323881(n) = v323881[n];
A353461(n) = sumdiv(n, d, A003602(d)*A323881(n/d));
CROSSREFS
Cf. A003602, A126760, A323881, A353460 (Dirichlet inverse), A353462 (sum with it).
Cf. also A349371, A349393.
Sequence in context: A118514 A190544 A172293 * A161970 A230446 A260737
KEYWORD
sign
AUTHOR
Antti Karttunen, Apr 20 2022
STATUS
approved