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A346243
Sum of A324198 and its Dirichlet inverse.
2
2, 0, 0, 1, 0, 6, 0, 1, 9, 2, 0, -1, 0, 2, 6, 1, 0, -15, 0, 9, 6, 2, 0, 1, 1, 2, -9, 1, 0, 44, 0, 1, 6, 2, 2, 15, 0, 2, 6, 5, 0, -4, 0, 1, 69, 2, 0, 1, 1, 57, 6, 1, 0, 45, 2, 1, 6, 2, 0, -49, 0, 2, -3, 1, 2, -4, 0, 1, 6, 20, 0, -3, 0, 2, 171, 1, 2, -4, 0, 5, 27, 2, 0, 15, 2, 2, 6, 1, 0, -235, 2, 1, 6, 2, 2, 1, 0, 13
OFFSET
1,1
FORMULA
a(n) = A324198(n) + A346242(n).
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];
A346243(n) = (A324198(n)+A346242(n));
CROSSREFS
KEYWORD
sign,base
AUTHOR
Antti Karttunen, Jul 13 2021
STATUS
approved