A069517 - OEIS

%I #22 Aug 29 2023 04:19:59

%S 1,2,0,2,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N a(n) = (-1)*Sum_{d|n} (moebius(d)*(-1)^d).

%C From _Andrew Howroyd_, Jul 25 2018: (Start)

%C Moebius transform of A037227.

%C Multiplicative because A037227 is. (End)

%H Antti Karttunen, <a href="/A069517/b069517.txt">Table of n, a(n) for n = 1..16384</a>

%F a(1) = 1 and for n>1, a(n) = 2*A209229(n). - corrected by _Antti Karttunen_, Nov 19 2017

%F Multiplicative with a(2^e) = 2 and a(p^e) = 0 for an odd prime p. - _Amiram Eldar_, Aug 29 2023

%t a[n_] := If[n == 2^IntegerExponent[n, 2], 2, 0]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Aug 29 2023 *)

%o (PARI) A069517(n) = (-1)*sumdiv(n,d,moebius(d)*((-1)^d)); \\ _Antti Karttunen_, Nov 19 2017

%o (PARI) a(n) = if(n == 1, 1, if(n >> valuation(n, 2) == 1, 2, 0)); \\ _Amiram Eldar_, Aug 29 2023

%Y Cf. A037227, A209229.

%K easy,nonn,mult

%O 1,2

%A _Benoit Cloitre_, Apr 16 2002