OFFSET
1,3
COMMENTS
LINKS
EXAMPLE
The ratio a(n)/A354828(n) for n = 1..21: 1, -1, -5/4, -2/7, -7/6, 5/4, -11/8, -8/35, -75/208, 7/6, -13/12, 5/14, -17/14, 11/8, 35/24, -1648/7595, -19/18, 75/208, -23/20, 1/3, 55/32.
PROG
(PARI)
up_to = 65537;
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
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.
AuxA354827(n) = (A003961(n)/sigma(n));
vDirInv = DirInverseCorrect(vector(up_to, n, AuxA354827(n)));
A354827(n) = numerator(vDirInv[n]);
A354828(n) = denominator(vDirInv[n]);
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Antti Karttunen, Jun 07 2022
STATUS
approved