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A081808
Numbers n such that the largest prime power in the factorization of n equals phi(n).
2
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
1,1
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
FORMULA
a(n) = 3*2^(n+1).
MATHEMATICA
Table[3*2^(n + 1), {n, 1, 30}] (* Stefan Steinerberger, Jun 17 2007 *)
NestList[2#&, 12, 30] (* Harvey P. Dale, Jun 05 2024 *)
PROG
(Magma) [3*2^(n + 1): n in [1..35]]; // Vincenzo Librandi, May 18 2011
CROSSREFS
Essentially the same as A007283 = 3*2^n.
Sequence in context: A270257 A367361 A180617 * A369798 A260261 A080495
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Apr 10 2003
STATUS
approved