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 1-1 of 1 results.

A306478 The phi-radical numbers: composite numbers m such that rad(phi(m)) = rad(m-1).

Original entry on oeis.org

1729, 2431, 6601, 9605, 10585, 12801, 15211, 30889, 46657, 69751, 88561, 92929, 105001, 159895, 272323, 368641, 460801, 534061, 610051, 622909, 950797, 992251, 1047619, 1372801, 1374895, 1745701, 1902691, 2210671, 2628073, 2704801, 3225601, 5629339, 5690251, 6840001, 9738751
Offset: 1

Views

Author

Amiram Eldar and Thomas Ordowski, Feb 18 2019

Keywords

Comments

Problem: are there infinitely many such numbers?
These numbers are odd squarefree. They contain many Carmichael numbers.
The smallest such semiprime is 1525781251 = 19531*78121, see A306479.

Links

Crossrefs

Cf. A000010, A002997, A007947, A055744 (rad(phi(n)) = rad(n)), A306479.

Programs

  • Mathematica
    rad[n_] := Times @@ (First@# & /@ FactorInteger@n); Select[Range[100000], CompositeQ[#] && rad[EulerPhi[#]] == rad[# - 1] &]
  • PARI
    rad(n) = factorback(factorint(n)[, 1]); \\ A007947
isok(m) = !isprime(m) && (rad(eulerphi(m)) == rad(m-1)); \\ Michel Marcus, Feb 18 2019
Showing 1-1 of 1 results.

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

Content is available under The OEIS End-User License Agreement.