A353569 - OEIS

%I #15 Feb 20 2023 12:26:51

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

%T 0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,

%U 0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1

%N a(n) = 1 if n is an odd number divisible by a square > 1, otherwise 0.

%H Antti Karttunen, <a href="/A353569/b353569.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.

%F a(n) = A000035(n) * A107078(n).

%F a(n) = A000035(n) - A323239(n).

%F a(n) <= A353626(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2 - 4/Pi^2 = 0.094715... . - _Amiram Eldar_, Jul 24 2022

%t a[n_] := If[OddQ[n] && !SquareFreeQ[n], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 24 2022 *)

%o (PARI) A353569(n) = ((n%2)&&!issquarefree(n));

%Y Characteristic function of A053850.

%Y Cf. A000035, A107078, A323239, A353626.

%K nonn

%O 1

%A _Antti Karttunen_, May 03 2022

%E Definition clarified by _Antti Karttunen_, Feb 19 2023