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A354823
Dirichlet inverse of A351083, where A351083(n) = gcd(n, A327860(n)), and A327860 is the arithmetic derivative of the primorial base exp-function.
8
1, -1, -1, -1, -1, 1, -7, -5, 0, 1, -1, 1, -1, 13, -3, -1, -1, -2, -1, -7, 13, 1, -1, 9, -24, 1, 0, 7, -1, 7, -1, 33, 1, -15, 9, -6, -1, 1, -11, 27, -1, -25, -1, -1, 4, 1, -1, 7, 48, 24, 1, -1, -1, 2, -3, 59, 1, 1, -1, 19, -1, 1, -12, 23, 1, -1, -1, 33, 1, -23, -1, -2, -1, 1, 52, 1, 7, 23, -1, -67, 0, 1, -1, -25
OFFSET
1,7
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A351083(n/d) * a(d).
PROG
(PARI)
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A351083(n) = gcd(n, A327860(n));
memoA354823 = Map();
A354823(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354823, n, &v), v, v = -sumdiv(n, d, if(d<n, A351083(n/d)*A354823(d), 0)); mapput(memoA354823, n, v); (v)));
CROSSREFS
Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms).
Sequence in context: A100976 A152627 A277067 * A241902 A356023 A113223
KEYWORD
sign
AUTHOR
Antti Karttunen, Jun 09 2022
STATUS
approved