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

1,1

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.

Links

Table of n, a(n) for n=1..61.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A005487 A291741 A084087 * A080327 A283485 A184778

Adjacent sequences: A175900 A175901 A175902 * A175904 A175905 A175906

Keyword

nonn

Author

Artur Jasinski, Oct 12 2010, Oct 21 2010

Extensions

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

Status

approved