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

Author

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

Keywords

• nonn

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

Crossrefs

Cf. A006881, A007304, A014574, A046386

Programs

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 *)