A354351 Dirichlet inverse of A108951, primorial inflation of n.

1, -2, -6, 0, -30, 12, -210, 0, 0, 60, -2310, 0, -30030, 420, 180, 0, -510510, 0, -9699690, 0, 1260, 4620, -223092870, 0, 0, 60060, 0, 0, -6469693230, -360, -200560490130, 0, 13860, 1021020, 6300, 0, -7420738134810, 19399380, 180180, 0, -304250263527210, -2520, -13082761331670030, 0, 0, 446185740, -614889782588491410

Offset: 1

Author

Antti Karttunen, Jun 05 2022

Keywords

• sign
• mult

Comments

Multiplicative with a(p^e) = 0 if e > 1, and -A034386(p) otherwise.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2355
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A008683, A013929 (positions of 0's), A034386, A108951, A354352.

Cf. also A347379, A354186, A354349, A354359, A354365, A354366.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) }; \\ From A108951
A354351(n) = (moebius(n)*A108951(n));

Formula

a(n) = A008683(n) * A108951(n).

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A108951(n/d) * a(d).

a(n) = A354352(n) - A108951(n).