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A070806 Cototient(totient(n))=A070556(n) is a power of 2 and n is a prime number. 4
3, 5, 7, 13, 17, 29, 97, 113, 193, 257, 449, 509, 769, 7937, 12289, 65537, 114689, 520193, 786433, 7340033, 8388593, 33292289, 33550337, 469762049, 2130706433, 3221225473, 8588886017, 137438691329, 206158430209 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
Powers of 2 observable in A070556[this sequence] = {1, 2, 4, 8, 16, 64, 128, 256, 512, 4096, 8192, 32768, 65536, 262144, 524288, ...}. For F(m), Fermat prime:phi[F(m)]=2^m, cototient[2^m]=2^(m-1); if n=113: phi[113]=112, cototient[112]=112-48=64, so 113 is in this sequence.
MATHEMATICA
Do[s= EulerPhi[n]-EulerPhi[EulerPhi[n]]; If[IntegerQ[Log[2, s]]&&PrimeQ[n], Print[n]], {n, 1, 10000000}]
PROG
(PARI) ispow2(n)=n==1<<valuation(n, 2);
forprime(p=2, 4e9, if(ispow2(p-1-eulerphi(p-1)), print1(p", "))) \\ Charles R Greathouse IV, May 17 2011
CROSSREFS
Sequence in context: A247018 A038929 A242755 * A339506 A178490 A182981
KEYWORD
nonn
AUTHOR
Labos Elemer, May 08 2002
EXTENSIONS
a(20)-a(27) from Donovan Johnson, Feb 06 2010
a(28)-a(29) from Charles R Greathouse IV, May 17 2011
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)