A140700 a(n) = n*A069158(n).

1, -2, -3, 0, -5, 6, -7, 0, 0, 10, -11, 0, -13, 14, 15, 0, -17, 0, -19, 0, 21, 22, -23, 0, 0, 26, 0, 0, -29, 30, -31, 0, 33, 34, 35, 0, -37, 38, 39, 0, -41, 42, -43, 0, 0, 46, -47, 0, 0, 0, 51, 0, -53, 0, 55, 0, 57, 58, -59, 0, -61, 62, 0, 0, 65, 66, -67, 0, 69, 70

Offset

1,2

Comments

Primes have negative signs in a(n). Differs from A055615 at a(30) = 30.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

a(n) = Product_{d|n} A140699(n,d).

Prog

(PARI) a(n) = { my(r=1); fordiv(n, d, r*=moebius(d)); r*n } \\ Andrew Howroyd, Sep 20 2025
(Python)
from sympy import mobius, isprime
def A140700(n): return 0 if not mobius(n) else -n if isprime(n) else n # Chai Wah Wu, Apr 26 2026

Crossrefs

Cf. A069158, A140699, A054524, A140256, A055615.

Sequence in context: A267186 A248092 A145105 * A055615 A378655 A366390

Adjacent sequences: A140697 A140698 A140699 * A140701 A140702 A140703

Keyword

sign,easy

Author

Mats Granvik and Gary W. Adamson, May 24 2008

Extensions

New name and a(49) onwards from Andrew Howroyd, Sep 20 2025

Status

approved