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A129297 Nonnegative integers m such that m^2-1 has no divisors d with 1

%I A129297 #13 Jun 18 2022 04:04:01
%S A129297 0,1,2,3,4,6,12,18,30,42,60,72,102,108,138,150,180,192,198,228,240,
%T A129297 270,282,312,348,420,432,462,522,570,600,618,642,660,810,822,828,858,
%U A129297 882,1020,1032,1050,1062,1092,1152,1230,1278,1290,1302,1320,1428,1452,1482,1488
%N A129297 Nonnegative integers m such that m^2-1 has no divisors d with 1<d<m-1.
%C A129297 Since m^2-1 = (m+1)(m-1), this sequence is just 0,1,2,3, and the average of twin prime pairs A014574.
%H A129297 Harvey P. Dale, <a href="/A129297/b129297.txt">Table of n, a(n) for n = 1..1000</a>
%F A129297 A129296(a(n)) = #{1, a(n)-1} = 2;
%F A129297 a(n) = A014574(n-4) for n>4.
%e A129297 {1,41,43,1763} is the set of divisors of 42^2-1, therefore 42 is a term, A129296(42) = #{1,41} = 2.
%t A129297 nniQ[n_]:=Count[Rest[Divisors[n^2-1]],_?(#<n-1&)]==0; Join[{0,1}, Select[ Range[2,1500],nniQ]] (* _Harvey P. Dale_, Aug 09 2015 *)
%t A129297 Select[Range[0, 1500], #<4 || And @@ PrimeQ[# + {-1, 1}] &] (* _Amiram Eldar_, Jun 18 2022 *)
%o A129297 (PARI) isA129297(n) = (n <= 3) || divisors(n^2-1)[2] >= n-1
%Y A129297 Cf. A014574, A129293, A129295, A129296.
%K A129297 nonn
%O A129297 1,3
%A A129297 _Reinhard Zumkeller_, Apr 09 2007