A176686 Numbers n such that n^2-1 are products of 3 distinct primes.

14, 16, 20, 22, 32, 36, 38, 40, 52, 54, 58, 66, 68, 70, 78, 84, 88, 90, 96, 110, 112, 114, 128, 130, 132, 140, 156, 158, 162, 178, 182, 200, 210, 212, 222, 234, 238, 250, 252, 258, 264, 268, 292, 294, 306, 308, 310, 318, 330, 336, 338, 354, 366, 372, 378, 380

Offset

1,1

Comments

14^2-1=195=3*5*13, 16^2-1=255=3*5*17, 20^2-1=399=3*7*19.

All terms are even since n^2-1 for n odd is a multiple of 4. If m is a term, then (m-1, m+1) contains one prime and one nonsquare semiprime. - Chai Wah Wu, Mar 28 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[6! ], Last/@FactorInteger[ #^2-1]=={1, 1, 1}&]
Sqrt[#+1]&/@Select[Sort[Times@@@Subsets[Prime[Range[100]], {3}]], IntegerQ[ Sqrt[#+1]]&] (* Harvey P. Dale, Jul 24 2016 *)

Crossrefs

Cf. A006881, A007304, A014574, A046386

Sequence in context: A327822 A102107 A217707 * A007935 A076055 A068653

Adjacent sequences: A176683 A176684 A176685 * A176687 A176688 A176689

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

Status

approved