A175903 Numbers n such that there is another number k such that n^2-1 and k^2-1 have the same set of prime factors.

4, 5, 7, 11, 13, 17, 19, 23, 25, 26, 29, 31, 34, 35, 37, 41, 43, 49, 51, 53, 55, 56, 59, 61, 65, 67, 71, 76, 79, 81, 83, 89, 91, 92, 97, 101, 109, 111, 113, 125, 127, 129, 131, 139, 149, 151, 155, 161, 169, 179, 181, 187, 191, 197, 199, 209, 223, 235, 239, 241, 251

Offset: 1

Author

Artur Jasinski, Oct 12 2010, Oct 21 2010

Keywords

• nonn

Comments

The difference from A175901 is that k may also be larger than n. So we obtain the sequence by building the union of the sets A175901 and A175902, and sorting.

Examples

			a(2)=5 because set of prime divisors of 5^2-1 =2^3*3 is {2,3}, the same as for example for 7^2-1 = 2^4*3.
		

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}]; Take[Union[bb,ff],100] (* Artur Jasinski *)

Extensions

Name improved by T. D. Noe, Nov 15 2010