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A359590
Absolute values of A355690, where A355690 is the Dirichlet inverse of the characteristic function of numbers not congruent to 2 mod 4.
8
1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1
OFFSET
1
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)
a(n) = A359605(n) + A359606(n) = A359603(n) mod 2. - Antti Karttunen, Jan 17 2023
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]))); };
CROSSREFS
Parity of A355690, and also its absolute values.
Parity of A359603 and A359604.
Sum of A359605 and A359606.
Cf. A152822, A359819 (Dirichlet inverse).
Cf. also A359834.
Sequence in context: A285341 A059778 A355690 * A104521 A317198 A354993
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jan 09 2023
STATUS
approved