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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]-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 * A284814 A228627 A178581

Adjacent sequences:  A104014 A104015 A104016 * A104018 A104019 A104020

KEYWORD

nonn,changed

AUTHOR

Max Alekseyev, Feb 25 2005

STATUS

approved

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Last modified June 24 07:19 EDT 2017. Contains 288697 sequences.