%I #19 Jul 24 2022 03:55:48

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

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

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

%N a(n) = 1 if n is a multiple of the square of an odd prime (equally: if the odd part of n is not squarefree), otherwise 0.

%H Antti Karttunen, <a href="/A353626/b353626.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) = A107078(A000265(n)).

%F a(n) = a(2n) = a(A000265(n)).

%F a(n) = 1 - A353627(n) = 1 - abs(A209635(n)).

%F For all n >= 1, a(n) >= A353625(n) and (1-a(n)) * A166486(n) = A008966(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - 8/Pi^2 = 0.189430... . - _Amiram Eldar_, Jul 24 2022

%t a[n_] := If[AnyTrue[FactorInteger[n/2^IntegerExponent[n, 2]][[;;, 2]], # > 1 &], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 24 2022 *)

%o (PARI) A353626(n) = !issquarefree(n>>valuation(n,2));

%Y Cf. A000265, A008966, A107078, A166486, A209635, A353625.

%Y Characteristic function of A038838, binary complement of A353627.

%Y After n=1 differs from A347246 for the next time at n=153, where a(153) = 1, while A347246(153) = 0.

%K nonn

%O 1

%A _Antti Karttunen_, May 02 2022