A175902 -id:A175902 - cp's OEIS frontend

A175901 Numbers n such that there exists a smaller number k such that k^2-1 has exactly the same set of distinct prime divisors as n^2-1.

7, 17, 19, 26, 31, 41, 49, 53, 55, 65, 71, 76, 97, 109, 127, 129, 161, 191, 197, 199, 209, 239, 241, 251, 271, 289, 295, 351, 391, 401, 433, 449, 485, 511, 575, 577, 626, 647, 649, 685, 701, 703, 721, 727, 799, 811, 881, 883, 901, 967, 989, 1025, 1055, 1079

Offset: 1

Artur Jasinski, Oct 11 2010

nonn

Cf. A175902 (for corresponding k).

aa = {}; bb = {}; Do[k = n^2 - 1; c = FactorInteger[k]; b = {}; Do[AppendTo[b, c[[m]][[1]]], {m, 1, Length[c]}]; If[Position[aa, b] != {}, AppendTo[bb, n], AppendTo[aa, b]], {n, 2, 10000}]; bb (*Artur Jasinski*)

isok(n) = {pfs = factor(n^2-1)[,1]; for (k = 2, n-1, if (factor(k^2-1)[,1] == pfs, return (1));); return (0);} \\ Michel Marcus, Nov 04 2013

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

Edited by N. J. A. Sloane, Oct 14 2010

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.

Original entry on oeis.org

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

Artur Jasinski, Oct 12 2010, Oct 21 2010

nonn

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.

			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.

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

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 *)

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

cp's OEIS Frontend

A175901 Numbers n such that there exists a smaller number k such that k^2-1 has exactly the same set of distinct prime divisors as n^2-1.

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