A359834 Parity of Dirichlet inverse of A359832, where A359832(n) = 1 if the 2-adic valuation of n is either 0 or odd, otherwise 0.

1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0

Offset

1

Links

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

Index entries for characteristic functions

Formula

Multiplicative with a(2^e) = 1 if e is not a multiple of 3, otherwise 0, and for odd primes p, a(p^e) = 1 if e = 1, otherwise 0.

a(n) = A359833(n) mod 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 52/(7*Pi^2) = 0.752671... . - Amiram Eldar, Jan 25 2023

Mathematica

f[p_, e_] := If[e == 1, 1, 0]; f[2, e_] := If[Divisible[e, 3], 0, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 25 2023 *)

Prog

(PARI) A359834(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k, 1], !!(f[k, 2]%3), (1==f[k, 2]))); };

Crossrefs

Cf. A359831, A359832.

Cf. also A359590.

Sequence in context: A351956 A092152 A350070 * A179775 A341952 A167686

Adjacent sequences: A359831 A359832 A359833 * A359835 A359836 A359837

Keyword

nonn,mult

Author

Antti Karttunen, Jan 25 2023

Status

approved