A175904 Numbers m for which the set of prime divisors of m^2-1 is unique.

2, 3, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 32, 33, 36, 38, 39, 40, 42, 44, 45, 46, 47, 48, 50, 52, 54, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 73, 74, 75, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 93, 94, 95, 96, 98, 99

Offset: 1

Author

Artur Jasinski, Oct 12 2010, Oct 21 2010

Keywords

• nonn

Comments

Complement of A175903. A proof for the presence of the first 63 terms (for which the largest prime divisor is < 100) follows along the lines of the comment in A175607.

Examples

			The unique prime factor sets are {3} (m=2), {2} (m=3), {5,7} (m=6), {3,7} (m=8), {2,5} (m=9) etc.
		

Crossrefs

Cf. A175607, A175901 - A175904, A181447 - A181471.

Programs

Mathematica

aa = {}; bb = {}; cc = {}; ff = {}; Do[k = n^2 - 1; kk = FactorInteger[k]; b = {}; Do[AppendTo[b, kk[[m]][[1]]], {m, 1, Length[kk]}]; dd = Position[aa, b]; If[dd == {}, AppendTo[cc, n]; AppendTo[aa, b], AppendTo[ff, n]; AppendTo[bb, cc[[dd[[1]][[1]]]]]], {n, 2, 1000000}]; jj=Table[n,{2,99}]; ss=Union[bb,ff]; Take[Complement[jj,ss],63] (*Artur Jasinski*)