A105570 - OEIS

%I #16 Feb 22 2024 02:05:58

%S 0,0,0,0,4,0,0,0,8,9,0,0,12,0,0,0,16,0,18,0,20,0,0,0,24,25,0,27,28,0,

%T 0,0,32,0,0,0,36,0,0,0,40,0,0,0,44,45,0,0,48,49,50,0,52,0,54,0,56,0,0,

%U 0,60,0,0,63,64,0,0,0,68,0,0,0,72,0,0,75,76,0,0,0,80,81,0,0,84,0,0,0,88,0

%N Nonsquarefree numbers in place: a(n) = n if n is not squarefree, 0 otherwise.

%H Antti Karttunen, <a href="/A105570/b105570.txt">Table of n, a(n) for n = 0..65537</a>

%F a(n) = n - abs(mu(n))*n.

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = (1 - 1/zeta(2))/2 = 0.1960364490... . - _Amiram Eldar_, Feb 22 2024

%t Table[If[SquareFreeQ[n],0,n],{n,0,100}] (* _Harvey P. Dale_, Aug 13 2016 *)

%o (PARI) A105570(n) = if(issquarefree(n),0,n); \\ _Antti Karttunen_, Jul 03 2018

%Y Cf. A005117, A008966, A013661, A305980.

%K easy,nonn

%O 0,5

%A _Paul Barry_, Apr 14 2005