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Search: id:A104017
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| A104017 |
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Devaraj numbers which are not Carmichael numbers. |
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+0
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; listen)
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OFFSET
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1,1
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COMMENT
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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 (MHasler(AT)univ-ag.fr), Apr 03 2009]
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LINKS
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A. K. Devaraj, Devaraj's 2nd Conjecture
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PROGRAM
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(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 (MHasler(AT)univ-ag.fr), Apr 03 2009]
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CROSSREFS
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Cf. A104016, A002997.
Sequence in context: A051346 A110375 A112441 this_sequence A067791 A067779 A082440
Adjacent sequences: A104014 A104015 A104016 this_sequence A104018 A104019 A104020
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KEYWORD
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hard,nonn
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AUTHOR
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Max Alekseyev (maxale(AT)gmail.com), Feb 25 2005
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