OFFSET
1,4
COMMENTS
Multiplicative because A057521 is.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
FORMULA
a(1) = 1; a(n) = -Sum_{d|n, d < n} A057521(n/d) * a(d).
Let p be a prime, B = 1 + p - 2*p^2 and C = sqrt(1 + 2*p - 3*p^2). Then the sequence is multiplicative with a(p^e) = ((B-C)*(p-1+C)^(e-1) - (B+C)*(p-1-C)^(e-1))/(2^e*C). - Sebastian Karlsson, Dec 02 2021
MATHEMATICA
f[p_, e_] := Module[{B = 1 + p - 2*p^2, C = Sqrt[1 + 2*p - 3*p^2]}, FullSimplify[((B - C)*(p - 1 + C)^(e - 1) - (B + C)*(p - 1 - C)^(e - 1))/(2^e*C)]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 24 2023 *)
PROG
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Nov 18 2021
STATUS
approved