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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified June 25 10:09 EDT 2021. Contains 345453 sequences. (Running on oeis4.)