login
A346235
Dirichlet inverse of A341530, gcd(n*sigma(A003961(n)), sigma(n)*A003961(n)).
6
1, -1, -2, 0, -2, -32, -4, -4, 3, 2, -2, 34, -2, -16, -112, 8, -2, 125, -4, 0, 8, 0, -6, -128, 3, -14, -8, -124, -2, 8, -2, -10, -4, 2, -320, 920, -2, -4, 4, 8, -2, 64, -4, -358, 430, -12, -6, 528, -3, -5, -352, 16, -6, -368, -48, 224, 0, 2, -2, 104, -2, -12, -12, 28, -4, 16, -4, 0, -36, 400, -2, -440, -2, -2, 450, 8, -248, 128
OFFSET
1,3
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.
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
v346235 = DirInverseCorrect(vector(up_to, n, A341530(n)));
A346235(n) = v346235[n];
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 11 2021
STATUS
approved