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A176686
Numbers n such that n^2-1 are products of 3 distinct primes.
3
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved