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%I #10 Jun 24 2014 01:08:14
%S 2,6,12,30,60,120,240,510,1020,2040,4080,8160,16320,32640,65280,
%T 131070,262140,524280,1048560,2097120,4194240,8388480,16776960,
%U 33553920,67107840,134215680,268431360,536862720,1073725440,2147450880,4294901760,8589934590
%N Largest solution of phi(x) = 2^n.
%C The ratio of adjacent terms is 2 except for five terms (if there are exactly five Fermat primes). - _T. D. Noe_, Jun 21 2012
%H T. D. Noe, <a href="/A058215/b058215.txt">Table of n, a(n) for n = 0..100</a>
%F Assuming there are only 5 Fermat primes (A019434), a(n)=2^(n-30)*(2^32-1) for n>=31.
%e For n=6, 2^n=64; the solutions of phi(x)=64 are {85,128,136,160,170,192,204,240}; the largest is a(6)=240.
%t phiinv[ n_, pl_ ] := Module[ {i, p, e, pe, val}, If[ pl=={}, Return[ If[ n==1, {1}, {} ] ] ]; val={}; p=Last[ pl ]; For[ e=0; pe=1, e==0||Mod[ n, (p-1)pe/p ]==0, e++; pe*=p, val=Join[ val, pe*phiinv[ If[ e==0, n, n*p/pe/(p-1) ], Drop[ pl, -1 ] ] ] ]; Sort[ val ] ]; phiinv[ n_ ] := phiinv[ n, Select[ 1+Divisors[ n ], PrimeQ ] ]; Table[ phiinv[ 2^n ][ [ -1 ] ], {n, 0, 30} ] (* phiinv[ n, pl ] = list of x with phi(x)=n and all prime divisors of x in list pl. phiinv[ n ] = list of x with phi(x)=n *)
%Y Cf. A000010, A001317, A003401, A004729, A019434, A045544, A047999, A053576, A054432, A058213, A058214.
%K nonn
%O 0,1
%A _Labos Elemer_, Nov 30 2000
%E Edited by _Dean Hickerson_, Jan 25 2002
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