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 A104017 Devaraj numbers (A104016) which are not Carmichael numbers. 5
 11305, 39865, 96985, 401401, 464185, 786961, 1106785, 1296505, 1719601, 1993537, 2242513, 2615977, 2649361, 2722681, 3165961, 3181465, 3755521, 4168801, 4229601, 4483297, 4698001, 5034601, 5381265, 5910121, 5977153, 7177105 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..500 PROG (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; 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)) ) (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)) \\ M. F. Hasler, Apr 03 2009 CROSSREFS Cf. A104016, A002997. Sequence in context: A252859 A177216 A112441 * A317400 A284814 A228627 Adjacent sequences:  A104014 A104015 A104016 * A104018 A104019 A104020 KEYWORD nonn AUTHOR Max Alekseyev, Feb 25 2005 STATUS approved

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Last modified April 8 18:43 EDT 2020. Contains 333323 sequences. (Running on oeis4.)