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A349352
Sum of A006368, "the amusical permutation", and its Dirichlet inverse.
4
2, 0, 0, 9, 0, 12, 0, 9, 4, 24, 0, 24, 0, 30, 16, 27, 0, 42, 0, 30, 20, 48, 0, 21, 16, 60, 20, 51, 0, 54, 0, 45, 32, 78, 40, 30, 0, 84, 40, 51, 0, 90, 0, 78, 52, 102, 0, 96, 25, 90, 52, 84, 0, 90, 64, 57, 56, 132, 0, 27, 0, 138, 74, 99, 80, 138, 0, 111, 68, 114, 0, 114, 0, 168, 68, 132, 80, 150, 0, 138, 61, 186, 0
OFFSET
1,1
COMMENTS
The first negative term is a(2520) = -918.
LINKS
FORMULA
a(n) = A006368(n) + A349351(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A006368(d) * A349351(n/d).
PROG
(PARI)
up_to = 20000;
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.
A006368(n) = ((3*n)+(n%2))\(2+((n%2)*2));
v349351 = DirInverseCorrect(vector(up_to, n, A006368(n)));
A349351(n) = v349351[n];
A349352(n) = (A006368(n)+A349351(n));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 15 2021
STATUS
approved