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%I #12 Feb 14 2014 21:03:04
%S 1,3,9,19,27,33,57,81,171,207,243,253,361,513,729,1083,1539,1791,1809,
%T 2187,2673,3249,3699,4617,5643,6561,6859,8303,9747,10449,11601,11913,
%U 13851,19683,20493,20577,29241,41193,41553,43263,46569,50301,59049
%N Numbers n such that n | 12^n + 11^n + 10^n + 9^n + 8^n + 7^n.
%t Select[ Range[ 10^6 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ], # ] == 0 & ]
%t Select[Range[60000],Divisible[Total[Table[PowerMod[i,n,n],{i,7,12}]], n]/.n->#&] (* _Harvey P. Dale_, Jun 23 2011 *)
%o (PARI) isA057257(n)=!sum(i=7,12,Mod(i,n)^n) \\ _Charles R Greathouse IV_, Jun 24 2011
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Sep 21 2000