A081808 Numbers n such that the largest prime power in the factorization of n equals phi(n).

12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472

Offset: 1

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn
• easy

Comments

All numbers 3*2^k k>=2 are in the sequence.

Let n=p^k*q where p^k is the largest prime power is the factorization of n and (p,q)=1. If n belongs to the sequence then p^k = phi(n) = (p-1)*p^(k-1)*phi(q), implying that p=2 (since p-1 cannot divide p^k for prime p>2). Then 2 = phi(q), implying that q=3. Therefore the terms are simply the sequence 3*2^n for n=2,3,... - Max Alekseyev, Mar 02 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2).

Crossrefs

Essentially the same as A007283 = 3*2^n.

Programs

Magma

[3*2^(n + 1): n in [1..35]]; // Vincenzo Librandi, May 18 2011

Mathematica

Table[3*2^(n + 1), {n, 1, 30}] (* Stefan Steinerberger, Jun 17 2007 *)
NestList[2#&,12,30] (* Harvey P. Dale, Jun 05 2024 *)

Formula

a(n) = 3*2^(n+1).