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A141702 a(n) is the number of Carmichael numbers of the form prime(n)*prime(n')*prime(n") with n > n' > n". 5

%I #8 Sep 25 2019 10:29:16

%S 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,

%T 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,

%U 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

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

%C 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).

%H Amiram Eldar, <a href="/A141702/b141702.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%o (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 }

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

%K easy,nonn

%O 1,7

%A _M. F. Hasler_, Jun 30 2008

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)