A068563 Numbers k such that 2^k == 4^k (mod k).

1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 42, 48, 54, 60, 64, 72, 80, 84, 96, 100, 108, 120, 126, 128, 136, 144, 156, 160, 162, 168, 180, 192, 200, 216, 220, 240, 252, 256, 272, 288, 294, 300, 312, 320, 324, 336, 342, 360, 378, 384, 400, 408, 420, 432, 440

Offset: 1

Author

Benoit Cloitre, Mar 25 2002

Keywords

• easy
• nonn

Comments

If k is in the sequence then 2k is also in the sequence, but the converse is not true.

Contains A124240 as a subsequence. Their difference is given by A124241. - T. D. Noe, May 30 2003

Also, integers k such that A007733(k) divides k. Also, integers k such that for every odd prime divisor p of k, A007733(p) = A002326((p-1)/2) divides k. Also, integers k such that A000265(k) divides 2^k-1. - Max Alekseyev, Aug 25 2013

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• Eric Weisstein's World of Mathematics, Carmichael Function.

Crossrefs

Cf. A000265, A002322, A002326, A007733, A124240, A124241.

Programs

Mathematica

Select[Range[500], PowerMod[2,#,# ] == PowerMod[4,#,# ] & ]

PARI

isok(k) = Mod(2, k)^k == Mod(4, k)^k; \\ Amiram Eldar, Apr 19 2025

Extensions

Comment and Mathematica program corrected by T. D. Noe, Oct 17 2008