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.

A184966 Numbers k such that k^k - 1 is squarefree.

Original entry on oeis.org

2, 3, 4, 6, 7, 11, 12, 14, 15, 16, 20, 22, 23, 27, 31, 34, 35, 36, 38, 39, 42, 43, 47, 52, 56, 58, 59, 60, 63, 66, 67, 70, 71, 72, 75, 78, 79, 83, 84, 86, 87, 88, 90, 92, 94, 95, 96, 102, 103, 104, 106, 107, 108, 110, 111, 112, 114, 115, 119, 123, 128, 131, 135, 138
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 19 2011

Keywords

Comments

3^3 - 1 = 26 = 2 * 13.
4^4 - 1 = 255 = 3 * 5 * 17.
6^6 - 1 = 46655 = 5 * 7 * 31 * 43.

Crossrefs

Cf. A005117, A048861, A184967.

Programs

  • Mathematica
    Select[Range@43, SquareFreeQ[#^# - 1] &]
  • PARI
    isok(k) = issquarefree(k^k-1); \\ Michel Marcus, Feb 22 2021

Extensions

a(23)-a(64) from Amiram Eldar, Feb 22 2021

A188047 Numbers k such that k^k-1 and k^k+1 are squarefree.

Original entry on oeis.org

2, 4, 6, 12, 16, 20, 22, 34, 36, 42, 52, 56, 58, 60, 66, 72, 78, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 128, 138, 140, 142, 144, 156, 158
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 19 2011

Keywords

Comments

From Kevin P. Thompson, May 03 2022: (Start)
a(39) >= 160 (160^160-1 is squarefree; 160^160+1 has no known square factors but is not completely factored).
162, 186, 198, and 256 are also terms in this sequence. (End)

Examples

			6 is a term since 6^6-1 = 46655 = 5*7*31*43 and 6^6+1 = 46657 = 13*37*97 are both squarefree.

Links

Crossrefs

Intersection of A184966 and A184967.
Cf. A005117.

Programs

  • Mathematica
    Select[Range@42,SquareFreeQ[#^#-1]&&SquareFreeQ[#^#+1]&]
  • PARI
    isok(k) = issquarefree(k^k-1) && issquarefree(k^k+1); \\ Michel Marcus, Feb 22 2021

Extensions

a(11)-a(25) from D. S. McNeil, Mar 22 2011
a(26)-a(31) from Amiram Eldar, Feb 22 2021
a(32)-a(38) (from FactorDB) added by Kevin P. Thompson, May 03 2022

A188049 Numbers k such that k^k-1 and k^k+1 are both not squarefree.

Original entry on oeis.org

17, 18, 19, 40, 49, 51, 53, 55, 69, 82, 89, 91, 97, 99, 117, 118
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 19 2011

Keywords

Examples

			17 is a term since 17^17-1 = 2^4*10949*1749233*2699538733 and 17^17+1 = 2*3^2*45957792327018709121.

Crossrefs

Cf. A005117, A013929, A184966, A184967, A188047.

Programs

  • Mathematica
    Select[Range@41,!(SquareFreeQ[#^#-1]||SquareFreeQ[#^#+1])&]
  • PARI
    isok(k) = ! issquarefree(k^k-1) && ! issquarefree(k^k+1); \\ Michel Marcus, Feb 22 2021

Extensions

a(5)-a(14) from D. S. McNeil, Mar 22 2011
a(15)-a(16) from Amiram Eldar, Feb 22 2021
Showing 1-3 of 3 results.

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

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