A325144 a(n) = - Sum_{d | n} (-1)^d *a(d) if n != 1, a(1) = 1.

0, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 3, 0, 1, 2, 1, 0, 3, 1, 1, 0, 2, 1, 4, 0, 1, 3, 1, 0, 3, 1, 3, 0, 1, 1, 3, 0, 1, 3, 1, 0, 8, 1, 1, 0, 2, 2, 3, 0, 1, 4, 3, 0, 3, 1, 1, 0, 1, 1, 8, 0, 3, 3, 1, 0, 3, 3, 1, 0, 1, 1, 8, 0, 3, 3, 1, 0, 8, 1, 1, 0, 3, 1

Offset

0,10

Links

Peter Luschny, Table of n, a(n) for n = 0..10000

Formula

a(4*n) = 0 for n >= 0.

a(2*n) = 0 for n <= 0.

if n is prime then a(n) = 1.

if n is squarefree then a(n) is odd (A005117).

if a(n) is even then n is not squarefree (A013929) (for n > 0).

Maple

a := proc(n) option remember; `if`(n = 1, 1,
-add((-1)^d*a(d), d = numtheory:-divisors(n) minus {n})) end:
seq(a(n), n = 0..86);

Prog

(Python)
from functools import lru_cache
from sympy import divisors
@lru_cache(maxsize=None)
def A325144(n): return sum(A325144(d) if d&1 else -A325144(d) for d in divisors(n, generator=True, proper=True)) if n-1 else 1 # Chai Wah Wu, Mar 29 2026

Crossrefs

Cf. A008683, A005117, A013929.

Sequence in context: A039803 A360118 A147809 * A328610 A217605 A096651

Adjacent sequences: A325141 A325142 A325143 * A325145 A325146 A325147

Keyword

nonn

Author

Peter Luschny, Apr 19 2019

Status

approved