Search: id:A104017
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%I A104017
%S A104017 11305,39865,96985,401401,464185,786961,1106785,1296505,1719601,1993537,
%T A104017 2242513,2615977,2649361,2722681,3165961,3181465,3755521,4168801,
%U A104017 4229601,4483297,4698001,5034601,5381265,5910121,5977153,7177105
%N A104017 Devaraj numbers which are not Carmichael numbers.
%C A104017 Counterexamples to sufficiency of the original Devaraj's 2nd Conjecture. 
               Devaraj numbers are given by A104016.
%C A104017 It is sufficient to scan only odd numbers (cf. A104016), which makes 
               the computation of the list twice as fast. [From M. F. Hasler (MHasler(AT)univ-ag.fr), 
               Apr 03 2009]
%H A104017 A. K. Devaraj, <a href="http://www.crorepatibaniye.com/failurefunctions/
               conjecture2.asp">Devaraj's 2nd Conjecture</a>
%o A104017 (PARI) { DNC() = for(n=2,10^8, f=factorint(n); if(vecmax(f[,2])>1,next); 
               f=f[,1]; r=length(f); if(r==1,next); Carmichael=1; d=f[1]-1; p=1; 
               for(i=1,r, d=gcd(d,f[i]-1); p*=f[i]-1; if((n-1)%(f[i]-1),Carmichael=0)); 
               if( ((n-1)^(r-2)*d^2)%p==0 && !Carmichael, print1(" ",n)) ) }
%o A104017 (PARI) forstep( n=3, 10^7, 2, vecmax((f=factor(n))[,2])>1 & next; #(f*=[1,
               -1]~)>1 | next; gcd(f)^2*(n-1)^(#f-2) % prod(i=1,#f,f[i]) & next; 
               for( i=1,#f, (n-1)%f[i] & !print1(n",") & break)) \\ [From M. F. 
               Hasler (MHasler(AT)univ-ag.fr), Apr 03 2009]
%Y A104017 Cf. A104016, A002997.
%Y A104017 Sequence in context: A051346 A110375 A112441 this_sequence A067791 A067779 
               A082440
%Y A104017 Adjacent sequences: A104014 A104015 A104016 this_sequence A104018 A104019 
               A104020
%K A104017 hard,nonn
%O A104017 1,1
%A A104017 Max Alekseyev (maxale(AT)gmail.com), Feb 25 2005

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