A078461 a(n) = 0 if n is divisible by the square of odd prime, a(n) = 1 if n is an odd squarefree number, a(n) = 2 otherwise.

1, 2, 1, 2, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 0, 2, 0, 2, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 0, 0, 0, 1, 2, 1, 2, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

Dirichlet g.f.: zeta(s)/zeta(2s)*2^s/(2^s-1). - Ralf Stephan, Jun 17 2007

Sum_{k=1..n} a(k) ~ 12*n / Pi^2. - Vaclav Kotesovec, Feb 02 2019

Multiplicative with a(2^e) = 2, and for an odd prime p a(p^e) = 1 if e = 1 and 0 otherwise. - Amiram Eldar, Aug 27 2023

Mathematica

f[p_, e_] := If[e == 1, 1, 0]; f[2, e_] := 2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 27 2023 *)

Prog

(PARI) a(n)=if(n<1, 0, direuler(p=2, n, if(p%2==1, 1+X, if(p%2, 1, (1+X)/(1-X))))[n])
(PARI) A078461(n) = (issquarefree(n/2^valuation(n, 2))*(2-(n%2))); \\ Antti Karttunen, Sep 27 2018

Crossrefs

Cf. A038838, A056911.

Sequence in context: A335885 A335875 A107279 * A341945 A280535 A221171

Adjacent sequences: A078458 A078459 A078460 * A078462 A078463 A078464

Keyword

mult,nonn,easy

Author

Benoit Cloitre, Dec 31 2002

Status

approved