cp's OEIS Frontend

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.

%I A141706 #11 Sep 25 2019 10:28:13
%S A141706 0,561,10585,52633,0,530881,7207201,1024651,1615681,5444489,471905281,
%T A141706 36765901,2489462641,564651361,958762729,17316001,178837201,
%U A141706 1574601601,7991602081,597717121,962442001,4461725581,167385219121,43286923681
%N 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.
%C A141706 Primes for which there are no such numbers (i.e. prime(n) such that a(n)=0) are given in A051663.
%H A141706 Amiram Eldar, <a href="/A141706/b141706.txt">Table of n, a(n) for n = 1..10000</a>
%H A141706 <a href="/index/Ca#Carmichael">OEIS index entries for Carmichael numbers</a>
%e A141706 a(1)=0 since there is no Carmichael number having prime(1)=2 as factor.
%e A141706 a(2)=561 since this is the largest (since only) Carmichael number of the form pqr with prime r>q>p=prime(2)=3.
%e A141706 a(5)=0 since there is no Carmichael number of the form pqr with prime r>q>p=prime(5)=11.
%o A141706 (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 ))}
%Y A141706 Cf. A002997, A051663, A135720, A141702-A141705.
%K A141706 nonn
%O A141706 1,2
%A A141706 _M. F. Hasler_, Jul 03 2008