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%I #14 Jun 24 2014 01:08:14
%S 3,13,35,105,231,581,1315,3225,6711,15221,32755,74505,154407,339397,
%T 718115,1589145,3243831,6946421,14482675,31259145,63894567,135588037,
%U 281203235,601400985,1219907127,2557715317,5267017715,11123540745,22600784679,47205887429
%N Sum of solutions of phi(x) = 2^n.
%C If there are only five Fermat primes, then a(n) = 2^(n-30) * 99852066765 for n > 31. - _T. D. Noe_, Jun 21 2012
%H T. D. Noe, <a href="/A058214/b058214.txt">Table of n, a(n) for n = 0..100</a>
%e For n=6, 2^n=64; the solutions of phi(x)=64 are {85,128,136,160,170,192,204,240}, whose sum is a(6)=1315.
%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[Plus@@phiinv[2^n], {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, A058215.
%K nonn
%O 0,1
%A _Labos Elemer_, Nov 30 2000
%E Edited by _Dean Hickerson_, Jan 25 2002
%E a(28)-a(29) from _Donovan Johnson_, Oct 22 2011
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