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A105570 Nonsquarefree numbers in place: a(n) = n if n is not squarefree, 0 otherwise.

%I A105570 #16 Feb 22 2024 02:05:58
%S A105570 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 A105570 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 A105570 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 A105570 Nonsquarefree numbers in place: a(n) = n if n is not squarefree, 0 otherwise.
%H A105570 Antti Karttunen, <a href="/A105570/b105570.txt">Table of n, a(n) for n = 0..65537</a>
%F A105570 a(n) = n - abs(mu(n))*n.
%F A105570 Sum_{k=1..n} a(k) ~ c * n^2, where c = (1 - 1/zeta(2))/2 = 0.1960364490... . - _Amiram Eldar_, Feb 22 2024
%t A105570 Table[If[SquareFreeQ[n],0,n],{n,0,100}] (* _Harvey P. Dale_, Aug 13 2016 *)
%o A105570 (PARI) A105570(n) = if(issquarefree(n),0,n); \\ _Antti Karttunen_, Jul 03 2018
%Y A105570 Cf. A005117, A008966, A013661, A305980.
%K A105570 easy,nonn
%O A105570 0,5
%A A105570 _Paul Barry_, Apr 14 2005