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A346242 Dirichlet inverse of A324198, where A324198(n) = gcd(n, A276086(n)). 20
1, -1, -3, 0, -1, 5, -1, 0, 6, -3, -1, -2, -1, 1, -9, 0, -1, -16, -1, 4, 3, 1, -1, 0, -24, 1, -12, 0, -1, 43, -1, 0, 3, 1, -5, 14, -1, 1, 3, 0, -1, -11, -1, 0, 54, 1, -1, 0, -6, 32, 3, 0, -1, 44, -3, -6, 3, 1, -1, -50, -1, 1, -24, 0, 1, -5, -1, 0, 3, -15, -1, -4, -1, 1, 96, 0, -5, -5, -1, 0, 24, 1, -1, 8, -3, 1, 3, 0, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = A346243(n) - A324198(n).
From Antti Karttunen, Jun 09 2022: (Start)
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A324198(n/d) * a(d).
For all n >= 1, A000035(a(n)) = A008966(n).
For all n >= 1, a(A045344(n)) = -1.
(End)
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.
A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
v346242 = DirInverseCorrect(vector(up_to, n, A324198(n)));
A346242(n) = v346242[n];
CROSSREFS
Cf. A008966 (parity of terms), A005117 (positions of odd terms), A013929 (of even terms), A045344 (of -1's, at least a subset of them), A354810 (of 0's), A354811 (of 1's), A354812 (of 2's), A354813 (of 3's), A354814 (of 4's), A354822 (of -2's).
Sequence in context: A179552 A119879 A115714 * A020768 A246182 A104544
KEYWORD
sign,base
AUTHOR
Antti Karttunen, Jul 13 2021
STATUS
approved

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Last modified July 13 12:36 EDT 2024. Contains 374284 sequences. (Running on oeis4.)