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A071404 Which nonsquarefree number is a square number? a(n)-th nonsquarefree number equals n^2, the n-th square. 1

%I

%S 1,3,5,9,13,18,25,31,39,46,55,66,76,86,99,112,125,142,157,172,187,206,

%T 225,244,264,285,307,328,353,377,400,429,453,480,507,534,562,593,623,

%U 656,691,725,762,795,831,867,904,941,977,1019,1059,1101,1145,1185,1226

%N Which nonsquarefree number is a square number? a(n)-th nonsquarefree number equals n^2, the n-th square.

%F A013929(a(n)) = A000290(n) = n^2.

%F a(n) = kn^2 + O(n), where k = 1 - 6/Pi^2. - _Charles R Greathouse IV_, Sep 13 2013

%e The first, 3rd, 5th, 9th, 13th nonsquarefree numbers are 4,9,16,25,36.

%o (PARI) lista(nn) = {sqfs = select(n->(1-issquarefree(n)), vector(nn, i, i)); for (i = 1, #sqfs, if (issquare(sqfs[i]), print1(i, ", ")););} \\ _Michel Marcus_, Sep 12 2013

%o (PARI) a(n)=n^2-sum(k=1, n, n^2\k^2*moebius(k)) \\ _Charles R Greathouse IV_, Sep 13 2013

%Y Cf. A005117, A013929, A000040, A000290, A071403.

%K nonn

%O 2,2

%A _Labos Elemer_, May 24 2002

%E Offset changed by _Charles R Greathouse IV_, Sep 13 2013

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Last modified January 21 16:54 EST 2020. Contains 331114 sequences. (Running on oeis4.)