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Search: id:A141706
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| A141706 |
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a(n) = largest Carmichael number of the form prime(n)*prime(n')*prime(n") with n < n' < n", or 0 if no such number exists. |
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+0
2
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| 0, 561, 10585, 52633, 0, 530881, 7207201, 1024651, 1615681, 5444489, 471905281, 36765901, 2489462641, 564651361, 958762729, 17316001, 178837201, 1574601601, 7991602081, 597717121, 962442001, 4461725581, 167385219121, 43286923681
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Primes for which there are no such numbers (i.e. prime(n) such that a(n)=0) are given in A051663.
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LINKS
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OEIS index entries for Carmichael numbers
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EXAMPLE
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a(1)=0 since there is no Carmichael number having prime(1)=2 as factor.
a(2)=561 since this is the largest (since only) Carmichael number of the form pqr with prime r>q>p=prime(2)=3.
a(5)=0 since there is no Carmichael number of the form pqr with prime r>q>p=prime(5)=11.
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PROGRAM
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(PARI) A141706(n) = { /* based on code by J.Brennen (jb AT brennen.net) */ local( V=[], B, p=prime(n), q, r); for( A=1, p-1, B=ceil((p^2+1)/A); while( 1, r=(p*B-p+A*B-B)/(A*B-p*p); q=(A*r-A+1)/p; q<=p && break; denominator(q)==1 && denominator(r)==1 && r>q && isprime(q) && isprime(r) && (p*q*r)%(p-1)==1 && V=concat(V, [p*q*r]); B++ )); if( V, vecmax( V ))}
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CROSSREFS
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Cf. A002997, A051663, A135720, A141702-A141705.
Sequence in context: A097130 A110889 A063400 this_sequence A083736 A006931 A097061
Adjacent sequences: A141703 A141704 A141705 this_sequence A141707 A141708 A141709
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (www.univ-ag.fr/~mhasler), Jul 03 2008
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