OFFSET
1,8
COMMENTS
Multiplicative because A295316 is.
LINKS
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A295316(n/d) * a(d).
Multiplicative with a(p^e) = (-1)^e * Fibonacci(e). - Sebastian Karlsson, Jul 24 2022
Sum_{k=1..n} abs(a(k)) ~ c * n, where c = Product_{primes p} (1 + 1/(p^3 - p^2 - p)) = 1.6256655992867552241340804110236555506570411887342367924818823782775... - Vaclav Kotesovec, Feb 27 2023
MATHEMATICA
s[n_] := If[AllTrue[FactorInteger[n][[;; , -1]], OddQ], 1, 0]; a[1] = 1; a[n_] := -DivisorSum[n, a[#]*s[n/#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Jul 21 2022 *)
PROG
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Jul 21 2022
STATUS
approved