cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A175902 Values of k in A175901.

Original entry on oeis.org

5, 5, 11, 4, 11, 29, 11, 25, 13, 23, 29, 34, 13, 89, 13, 51, 11, 151, 43, 89, 181, 169, 89, 29, 101, 59, 223, 111, 181, 269, 125, 29, 23, 101, 83, 35, 56, 305, 79, 113, 181, 287, 151, 155, 379, 349, 769, 545, 329, 505, 571, 37, 373, 769, 344, 91, 1121, 79, 353, 79, 985
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2010, Oct 21 2010

Keywords

Crossrefs

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

Programs

  • PARI
    isok(n) = {pfs = factor(n^2-1)[,1]; for (k = 2, n-1, if (factor(k^2-1)[,1] == pfs, return (k));); return (0);}
lista(nn) = {for(n=2, nn, if (k = isok(n), print1(k, ", ");););} \\ Michel Marcus, Nov 04 2013

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Oct 12 2010, Oct 21 2010

Keywords

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*)

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

Views

Author

Artur Jasinski, Oct 12 2010, Oct 21 2010

Keywords

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
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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