A372568 a(n) = Sum_{d|n} A346242(d), where A346242 is the Dirichlet inverse of gcd(n, A276086(n)).

1, 0, -2, 0, 0, 2, 0, 0, 4, -4, 0, 0, 0, 0, -12, 0, 0, -8, 0, 0, 0, 0, 0, 0, -24, 0, -8, 0, 0, 32, 0, 0, 0, 0, -6, 4, 0, 0, 0, 0, 0, -6, 0, 0, 48, 0, 0, 0, -6, 4, 0, 0, 0, 24, -4, -6, 0, 0, 0, -16, 0, 0, -18, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 60, 0, -6, 0, 0, 0, 16, 0, 0, 0, -4, 0, 0, 0, 0, -160, -6, 0, 0, 0, 0, 0, 0, -42

Offset

1,3

Comments

No odd terms after the initial 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial base

Prog

(PARI)
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); };
memoA346242 = Map();
A346242(n) = if(1==n, 1, my(v); if(mapisdefined(memoA346242, n, &v), v, v = -sumdiv(n, d, if(d<n, A324198(n/d)*A346242(d), 0)); mapput(memoA346242, n, v); (v)));
A372568(n) = sumdiv(n, d, A346242(d));

Crossrefs

Inverse Möbius transform of A346242.

Cf. A276086, A324198.

Sequence in context: A138805 A316400 A061897 * A047919 A272624 A271223

Adjacent sequences: A372565 A372566 A372567 * A372569 A372570 A372571

Keyword

sign

Author

Antti Karttunen, May 24 2024

Status

approved