A141702 a(n) is the number of Carmichael numbers of the form prime(n)*prime(n')*prime(n") with n > n' > n".

0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 3, 1, 2, 0, 0, 0, 0, 1

Offset

1,7

Comments

The formula and PARI code uses Korselt's criterion. This sequence is a somewhat trivial variant of the more interesting sequence giving the number of Carmichael numbers of the form prime(n)*prime(n')*prime(n") with n < n' < n" (known to be finite for given n).

Links

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

Formula

a(n) = # { pqr | p=prime(n) > q=prime(n') > r=prime(n") ; p-1 | pqr-1 ; q-1 | pqr-1 ; r-1 | pqr-1 }

Example

a(7)=2 is the first nonzero term since 561 = 3*11*17 and 1105 = 5*13*17 are the two smallest Carmichael numbers and there's no other Carmichael number having prime(7)=17 as largest factor.

Prog

(PARI) A141702(n) = { local( p=prime(n), c=0 ); forprime( q=5, p-2, forprime( r=3, q-2, (p*q*r-1)%(p-1)==0 && (p*q*r-1)%(q-1)==0 && (p*q*r-1)%(r-1)==0 && c++ )); c }

Crossrefs

Cf. A002997 and references therein ; A087788 ; A141703 ff.

Sequence in context: A257265 A045706 A045634 * A364048 A353657 A259896

Adjacent sequences: A141699 A141700 A141701 * A141703 A141704 A141705

Keyword

easy,nonn

Author

M. F. Hasler, Jun 30 2008

Status

approved