OFFSET
1
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
FORMULA
Multiplicative with a(2^e) = 1 if e mod 3 == 0 or 2, otherwise 0, and for odd primes p, a(p^e) = 1 if e = 1, otherwise 0.
a(n) = abs(A355690(n)).
From Amiram Eldar, Jan 11 2023: (Start)
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 40/(7*Pi^2) = 0.578978... .
Dirichlet g.f.: (zeta(s)/zeta(2*s))*(16^s+4^s)/((2^s+1)*(8^s-1)). (End)
MATHEMATICA
f[p_, e_] := If[e == 1, 1, 0]; f[2, e_] := If[Mod[e, 3] == 1, 0, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 11 2023 *)
PROG
(PARI) A359590(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k, 1], !(1==(f[k, 2]%3)), (1==f[k, 2]))); };
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jan 09 2023
STATUS
approved