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

0, 1, 2, 3, 4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150, 180, 192, 198, 228, 240, 270, 282, 312, 348, 420, 432, 462, 522, 570, 600, 618, 642, 660, 810, 822, 828, 858, 882, 1020, 1032, 1050, 1062, 1092, 1152, 1230, 1278, 1290, 1302, 1320, 1428, 1452, 1482, 1488

Offset: 1

Author

Reinhard Zumkeller, Apr 09 2007

Keywords

• nonn

Comments

Since m^2-1 = (m+1)(m-1), this sequence is just 0,1,2,3, and the average of twin prime pairs A014574.

Examples

			{1,41,43,1763} is the set of divisors of 42^2-1, therefore 42 is a term, A129296(42) = #{1,41} = 2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A014574, A129293, A129295, A129296.

Programs

Mathematica

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 *)
Select[Range[0, 1500], #<4 || And @@ PrimeQ[# + {-1, 1}] &] (* Amiram Eldar, Jun 18 2022 *)

PARI

isA129297(n) = (n <= 3) || divisors(n^2-1)[2] >= n-1

Formula

A129296(a(n)) = #{1, a(n)-1} = 2;

a(n) = A014574(n-4) for n>4.