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%I #19 Feb 14 2021 12:59:31
%S 1,12,24,36,48,72,96,108,120,144,192,216,240,288,324,336,360,384,432,
%T 480,576,600,648,672,720,768,864,960,972,1008,1080,1152,1200,1296,
%U 1344,1440,1536,1728,1800,1920,1944,2016,2160,2304,2352,2400,2448,2592,2688
%N Numbers k such that Sum_{d|k} d^2*mu(d) divides k^2.
%C If n > 1, a(n+1) - a(n) == 0 (mod 12), so a(n+1) - a(n) = 12 for n=2,3,4,5,7,8,...; a(n+1) - a(n) = 24 for n=6,9,.... Conjecture: if c > 2 and n > 1, Sum_{d|n} d^c*mu(d) never divides n^c. Hence A063453(n) never divides n^3 for n > 1.
%H Reinhard Zumkeller, <a href="/A069056/b069056.txt">Table of n, a(n) for n = 1..1000</a>
%F Numbers k such that A046970(k) divides k.
%t f[d_] := d^2*MoebiusMu[d]; ok[n_] := Divisible[n^2, Total[f /@ Divisors[n]]]; Select[Range[3000], ok] (* _Jean-François Alcover_, Nov 15 2011 *)
%o (PARI) for(n=1,1000,if(n^2%sumdiv(n,d,moebius(d)*d^2)==0,print1(n,",")))
%o (Haskell)
%o a069056 n = a069056_list !! (n-1)
%o a069056_list = filter (\x -> x ^ 2 `mod` a046970 x == 0) [1..]
%o -- _Reinhard Zumkeller_, Jan 19 2012
%K easy,nice,nonn
%O 1,2
%A _Benoit Cloitre_, Apr 07 2002
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