A141705 a(n) is the least Carmichael number of the form prime(n)*prime(n')*prime(n") with n < n' < n", or 0 if no such number exists.
0, 561, 1105, 1729, 0, 29341, 162401, 334153, 1615681, 3581761, 399001, 294409, 252601, 1152271, 104569501, 2508013, 178837201, 6189121, 10267951, 10024561, 14469841, 4461725581, 985052881, 19384289, 23382529, 3828001, 90698401
Offset: 1
Keywords
Examples
a(1)=0 since there is no Carmichael number having prime(1)=2 as factor. a(2)=561 since this is the smallest 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.
Links
Programs
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PARI
A141705(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, vecmin( V )); }
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