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%I #18 Jul 27 2016 10:21:07
%S 1,1,1,2,3,3,3,7,3,5
%N Number of prime factors (with multiplicity) of generalized Fermat number 6^(2^n) + 1.
%F a(n) = A001222(A078303(n)). - _Felix Fröhlich_, Jul 25 2016
%e b(n) = 6^(2^n) + 1.
%e Complete Factorizations
%e b(0) = 7
%e b(1) = 37
%e b(2) = 1297
%e b(3) = 17*98801
%e b(4) = 353*1697*4709377
%e b(5) = 2753*145601*19854979505843329
%e b(6) = 4926056449*447183309836853377*28753787197056661026689
%e b(7) = 257*763649*50307329*3191106049*2339340566463317436161*
%e 2983028405608735541756929*18247770097021321924017185281
%e b(8) = 18433*
%e 69615986569139423375849495295909549956813828853888948633601*P137
%e b(9) = 80897*3360769*12581314681802812884728041373153281*
%e 3513902440204553274892072241244613302018049*P311
%t Table[PrimeOmega[6^(2^n) + 1], {n, 0, 6}] (* _Michael De Vlieger_, Jul 26 2016 *)
%o (PARI) a(n) = bigomega(factor(6^(2^n)+1))
%Y Cf. A078303, A273947.
%K nonn,hard,more
%O 0,4
%A _Arkadiusz Wesolowski_, Jul 25 2016
%E a(8) was found in 2001 by Robert Silverman
%E a(9) was found in 2007 by Nestor de Araújo Melo