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%I A049532 #49 Sep 08 2022 08:44:58
%S A049532 7,18,32,38,41,43,57,68,70,82,93,99,107,117,118,132,143,157,168,182,
%T A049532 193,207,218,232,239,243,251,257,268,282,293,307,318,327,332,343,357,
%U A049532 368,378,382,393,407,408,418,432,437,443,457,468,482,493,500,507,515
%N A049532 Numbers k such that k^2 + 1 is not squarefree.
%C A049532 The sequence is infinite. For instance, it contains all numbers of the form 7 + 25m. - _Emmanuel Vantieghem_, Oct 25 2016
%C A049532 More generally, the sequence contains all numbers of the form a(n) + (a(n)^2 + 1) * m for even a(n) and a(n) + (a(n)^2 + 1) * m / 2 for odd a(n). - _David A. Corneth_, Oct 25 2016
%C A049532 The asymptotic density of this sequence is 1 - A335963 = 0.1051587754... - _Amiram Eldar_, Jul 08 2020
%H A049532 R. J. Mathar, <a href="/A049532/b049532.txt">Table of n, a(n) for n = 1..7999</a>
%F A049532 A059592(a(n)) > 1; A124809(n) = a(n)^2 + 1. - _Reinhard Zumkeller_, Nov 08 2006
%e A049532 a(1) = 7 because 7^2 + 1 = 49 + 1 = 50 is divisible by 25, a square.
%t A049532 n=1;Reap[Do[While[SquareFreeQ[n^2+1],n++];Sow[n];n++,{c,10000}]][[2,1]] (* _Zak Seidov_, Feb 24 2011 *)
%o A049532 (PARI) for(n=1,1e4,if(!issquarefree(n^2+1),print1(n", "))) \\ _Charles R Greathouse IV_, Feb 24 2011
%o A049532 (Magma) [n: n in [1..6*10^2]| not IsSquarefree(n^2+1)]; // _Bruno Berselli_, Oct 15 2012
%Y A049532 Cf. A002522, A059592, A124809, A335963.
%K A049532 nonn
%O A049532 1,1
%A A049532 _Labos Elemer_
%E A049532 Definition rewritten by _Bruno Berselli_, Oct 15 2012
%E A049532 Mathematica updated by _Jean-François Alcover_, Jun 19 2013

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