OFFSET
0,2
COMMENTS
n = 32 is the first place where this differs from A001317, since 2^32 + 1 is not prime. - Mitch Harris, May 02 2007
a(8589934592) is the first unknown term; it is 2^8589934593 if F(33) = 2^(2^33)+1 is composite or F(33) otherwise. - Charles R Greathouse IV, Jul 15 2013
a(n) is the only odd element of the set phi-1(2^n), the totient inverses of 2^n. All other elements are 2*a(n), and the even elements of phi-1(2^(n-1)) * 2. - Torlach Rush, Sep 05 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..3320
EXAMPLE
1,2,4,8,...,131072 divide phi of 2,3,5,15,...,196611 = 3*65537 respectively.
MATHEMATICA
With[{s = Array[EulerPhi, 10^6]}, Table[FirstPosition[s, _?(Divisible[#, 2^n] &)][[1]], {n, 0, 19}]] (* Michael De Vlieger, Sep 05 2017 *)
PROG
(PARI) a(n)={
if(n >= 8589934592 && valuation(n>>5, 2)>27,
warning("Result is conjectural on the nonexistence of Fermat primes >= F(33).")
);
if(n>31,
return(2<<n)
);
n=binary(n);
prod(i=1, #n, (2^2^(i-1)+1)^n[#n+1-i])
}; \\ Charles R Greathouse IV, Jul 15 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 18 2000
EXTENSIONS
More odd terms from Jud McCranie, Jan 25 2000
STATUS
approved