OFFSET
1,2
COMMENTS
This is not multiplicative because A344695 is not multiplicative. The first point where a(m*n) = a(m)*a(n) does not hold for coprime m and n is 108 = 4*27, where a(108) = -484 <> -480 = 8 * -60 = a(4) * a(27).
Conjecture: No zeros occur as terms. Checked up to n = 2^21.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..12000
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.
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
v347228 = DirInverseCorrect(vector(up_to, n, A344695(n)));
A347228(n) = v347228[n];
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Aug 25 2021
STATUS
approved