A358766 a(n) = lambda(sigma(n)), where lambda is Liouville's lambda, and sigma is the sum of divisors function.

1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences related to sigma(n)

Formula

Multiplicative with a(p^e) = (-1)^A001222(1 + p + p^2 + ... + p^e).

a(n) = A008836(A000203(n)) = (-1)^A001222(A000203(n)) = (-1)^A058063(n).

a(n) = A008836(n) / A359166(n) = A359166(n) / A008836(n).

Prog

(PARI) A358766(n) = ((-1)^bigomega(sigma(n)));
(Python)
from functools import reduce
from operator import ixor
from collections import Counter
from sympy import factorint
def A358766(n): return -1 if reduce(ixor, sum((Counter(factorint((p**(e+1)-1)//(p-1))) for p, e in factorint(n).items()), Counter()).values(), 0)&1 else 1 # Chai Wah Wu, Dec 23 2022

Crossrefs

Cf. A000203, A001222, A008836, A058063, A358767 (positions of positive terms), A358768 (of negative terms).

Cf. also A359166.

Sequence in context: A158388 A162285 A186035 * A359154 A359166 A359581

Adjacent sequences: A358763 A358764 A358765 * A358767 A358768 A358769

Keyword

sign,mult

Author

Antti Karttunen, Dec 18 2022

Status

approved