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.

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A319370 Composite numbers k such that phi(k)^phi(k) == k + 1 (mod k^2).

Original entry on oeis.org

91, 18227, 28605, 137481, 538849, 2832797, 3220333, 384792005
Offset: 1

Views

Author

Altug Alkan, Sep 17 2018

Keywords

Comments

Composite numbers k such that (k-phi(k))^phi(k) == 1 (mod k^2).

Crossrefs

Programs

  • PARI
    isok(n) = n>1 && !isprime(n) && Mod(n-eulerphi(n), n^2)^eulerphi(n)==1;

A319383 Numbers k such that phi(k)^phi(k) == 1 (mod k^2).

Original entry on oeis.org

1, 2, 19043, 289627, 6674419, 49865347, 185014655
Offset: 1

Views

Author

Altug Alkan, Sep 18 2018

Keywords

Comments

All terms are cyclic numbers (A003277).
The next term, if it exists, is > 10^10. - Vaclav Kotesovec, Oct 23 2018
a(8) > 10^12, if it exists. - Giovanni Resta, Oct 25 2018

Crossrefs

Programs

  • Mathematica
    Select[Range[20000], Divisible[EulerPhi[#]^EulerPhi[#] - 1, #^2] &] (* Vaclav Kotesovec, Oct 21 2018 *)
    Join[{1},Select[Range[1851*10^5],With[{c=EulerPhi[#]},PowerMod[c,c,#^2] == 1&]]] (* Harvey P. Dale, Oct 09 2020 *)
  • PARI
    isok(n) = Mod(eulerphi(n), n^2)^eulerphi(n)==1;
    for(n=1, 10000000, if(isok(n),print1(n, ", ")))

A319505 Numbers k such that 2^(k*(k+1)/2) == -1 (mod k^2).

Original entry on oeis.org

1, 389993, 476729, 2927297, 3048569, 3862529, 3914049, 4755729, 5077209, 7460409, 9009489, 9314009, 11066649, 11981409, 12928289, 13342769, 15371609, 15574449, 22975249, 34429449, 44876649, 57046209, 66358417, 66963369, 79552209, 83006769, 96783929, 99127313, 118462737, 126209609, 128566689, 139745969
Offset: 1

Views

Author

Altug Alkan, Sep 21 2018

Keywords

Crossrefs

Programs

  • PARI
    isok(n) = Mod(2, n^2)^(n*(n+1)/2)==-1;
Previous Showing 21-23 of 23 results.