A354823 Dirichlet inverse of A351083, where A351083(n) = gcd(n, A327860(n)), and A327860 is the arithmetic derivative of the primorial base exp-function.

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..30030

Index entries for sequences related to primorial base

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. A327860, A351083.

Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms).

Cf. also A346242, A354347, A354348, A354824.

Sequence in context: A100976 A152627 A277067 * A241902 A356023 A113223

Adjacent sequences: A354820 A354821 A354822 * A354824 A354825 A354826

Keyword

sign

Author

Antti Karttunen, Jun 09 2022

Status

approved