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A354824
Dirichlet inverse of A351084, where A351084(n) = gcd(n, A328572(n)), and A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.
5
1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, -3, 0, -1, 0, -1, -4, 1, 1, -1, 0, -24, 1, 0, 0, -1, 7, -1, 0, 1, 1, 1, 0, -1, 1, 1, 8, -1, -1, -1, 0, 4, 1, -1, 0, 0, 24, 1, 0, -1, 0, -3, 0, 1, 1, -1, 4, -1, 1, -6, 0, 1, -1, -1, 0, 1, -7, -1, 0, -1, 1, 52, 0, -5, -1, -1, -8, 0, 1, -1, -6, -3, 1, 1, 0, -1, -8, -5, 0
OFFSET
1,15
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A351084(n/d) * a(d).
PROG
(PARI)
A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
A351084(n) = gcd(n, A328572(n));
memoA354824 = Map();
A354824(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354824, n, &v), v, v = -sumdiv(n, d, if(d<n, A351084(n/d)*A354824(d), 0)); mapput(memoA354824, n, v); (v)));
CROSSREFS
Cf. A351084.
Sequence in context: A316896 A230626 A363946 * A183700 A275478 A248678
KEYWORD
sign
AUTHOR
Antti Karttunen, Jun 09 2022
STATUS
approved