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A104017
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Devaraj numbers which are not Carmichael numbers.
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4
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Counterexamples to sufficiency of the original Devaraj's 2nd Conjecture. Devaraj numbers are given by A104016.
It is sufficient to scan only odd numbers (cf. A104016), which makes the computation of the list twice as fast. [From M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 03 2009]
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LINKS
| A. K. Devaraj, Devaraj's 2nd Conjecture
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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]-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)) \\ [From M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 03 2009]
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CROSSREFS
| Cf. A104016, A002997.
Sequence in context: A110375 A177216 A112441 * A178581 A178583 A178589
Adjacent sequences: A104014 A104015 A104016 * A104018 A104019 A104020
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KEYWORD
| hard,nonn
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AUTHOR
| Max Alekseyev (maxale(AT)gmail.com), Feb 25 2005
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