%I
%S 11305,39865,96985,401401,464185,786961,1106785,1296505,1719601,
%T 1993537,2242513,2615977,2649361,2722681,3165961,3181465,3755521,
%U 4168801,4229601,4483297,4698001,5034601,5381265,5910121,5977153,7177105
%N Devaraj numbers (A104016) which are not Carmichael numbers.
%C Counterexamples to Devaraj's 2nd conjecture: _A.K. Devaraj_ conjectured that these numbers are exactly Carmichael numbers. It was proved (see A104016 ) that every Carmichael number is indeed a Devaraj number, but the converse is not true. Devaraj numbers that are not Carmichael are listed here.
%C It is sufficient to scan only odd numbers (cf. A104016), which makes the computation of the list twice as fast.  _M. F. Hasler_, Apr 03 2009
%H Charles R Greathouse IV, <a href="/A104017/b104017.txt">Table of n, a(n) for n = 1..500</a>
%o (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((n1)%(f[i]1),Carmichael=0)); if( ((n1)^(r2)*d^2)%p==0 && !Carmichael, print1(" ",n)) )
%o (PARI) forstep( n=3, 10^7, 2, vecmax((f=factor(n))[,2])>1 && next; #(f*=[1,1]~)>1  next; gcd(f)^2*(n1)^(#f2) % prod(i=1,#f,f[i]) && next; for( i=1,#f, (n1)%f[i] && !print1(n",") && break)) \\ _M. F. Hasler_, Apr 03 2009
%Y Cf. A104016, A002997.
%K nonn
%O 1,1
%A _Max Alekseyev_, Feb 25 2005
