A141706 a(n) is the largest Carmichael number of the form prime(n)*prime(n')*prime(n") with n < n' < n", or 0 if no such number exists.

0, 561, 10585, 52633, 0, 530881, 7207201, 1024651, 1615681, 5444489, 471905281, 36765901, 2489462641, 564651361, 958762729, 17316001, 178837201, 1574601601, 7991602081, 597717121, 962442001, 4461725581, 167385219121, 43286923681

Offset

1,2

Comments

Primes for which there are no such numbers (i.e. prime(n) such that a(n)=0) are given in A051663.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

OEIS index entries for Carmichael numbers

Example

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.

Prog

(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 ))}

Crossrefs

Cf. A002997, A051663, A135720, A141702-A141705.

Sequence in context: A339875 A290945 A063400 * A290485 A213071 A232761

Adjacent sequences: A141703 A141704 A141705 * A141707 A141708 A141709

Keyword

nonn

Author

M. F. Hasler, Jul 03 2008

Status

approved