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%I #15 Sep 08 2022 08:46:04
%S 117,407,606,775,943,1193,1252,1482,1743,1957,2267,2563,3217,3281,
%T 3309,3457,3506,3618,3718,3817,4007,4632,4831,5168,5742,5743,5845,
%U 6031,6182,6492,6768,7506,7843,8042,8118,8331,8368,8418,8707,8782,8857,9056,9292,9393
%N Numbers n such that n^2 + 1 and (n+1)^2 + 1 are divisible by a square.
%C Also numbers n such that mu(n^2+1) = mu((n+1)^2+1)=0, where mu is the Moebius-function (A008683).
%H Vincenzo Librandi, <a href="/A217798/b217798.txt">Table of n, a(n) for n = 1..1000</a>
%e 117 is in the sequence because 117^2+1 = 2*5*37^2 and 118^2+1 = 5^2*557.
%p with(numtheory):for n from 1 to 10000 do :x:=n^2+1:y:=(n+1)^2+1:if issqrfree(x)=false and issqrfree(y)=false then printf(`%d, `,n):else fi:od:
%t Select[ Range[2, 10000], Max[ Transpose[ FactorInteger[ #^2+1 ]] [[2]]] > 1 && Max[ Transpose[ FactorInteger[ (#+1)^2 + 1]] [[2]]] > 1 &]
%o (Magma) A002522:=func<m | m^2+1>; [n: n in [1..10^4]| not IsSquarefree(A002522(n)) and not IsSquarefree(A002522(n+1))]; // _Bruno Berselli_, Oct 15 2012
%Y Cf. A002522, A068781.
%Y Subsequence of A049532.
%K nonn
%O 1,1
%A _Michel Lagneau_, Oct 12 2012
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