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A346480
Sum of A250469 and its Dirichlet inverse.
4
2, 0, 0, 9, 0, 30, 0, 27, 25, 42, 0, 45, 0, 66, 70, 45, 0, 75, 0, 99, 110, 78, 0, 3, 49, 102, 125, 135, 0, 60, 0, 81, 130, 114, 154, -39, 0, 138, 170, 15, 0, 60, 0, 261, 175, 174, 0, 117, 121, 231, 190, 297, 0, -225, 182, 3, 230, 186, 0, -381, 0, 222, 275, 189, 238, 360, 0, 423, 290, 216, 0, 381, 0, 246, 245, 459
OFFSET
1,1
FORMULA
a(n) = A250469(n) + A346479(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A250469(d) * A346479(n/d).
PROG
(PARI)
up_to = 16384;
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.
v346479 = DirInverseCorrect(vector(up_to, n, A250469(n)));
A346479(n) = v346479[n];
A346480(n) = (A250469(n)+A346479(n));
(PARI) A346480(n) = if(1==n, 2, -sumdiv(n, d, if((1==d)||n==d, 0, A250469(d)*A346479(n/d)))); \\ (Demonstrates the convolution formula).
CROSSREFS
Cf. also A346478.
Sequence in context: A347229 A347095 A346255 * A323399 A246714 A246708
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 30 2021
STATUS
approved