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%I A193873 #20 May 13 2013 01:54:20
%S A193873 30,105,1729,1105,13981,1729,88537,50881,51319,13981,137149,29341,
%T A193873 548497,88537,285541,186337,3372529,51319,18326641,252601,1152271,
%U A193873 137149,1809641,1366633,3828001,548497,4814857,645569,4797703,285541,79230049,4811297
%N A193873 Smallest product of three distinct primes of the form n*k+1.
%C A193873 Note that the Hardy-Ramanujan is the first and the smallest repeated number: a(3)=a(6)=1729.
%H A193873 Charles R Greathouse IV, <a href="/A193873/b193873.txt">Table of n, a(n) for n = 1..10000</a>
%e A193873 a(1) =  2*3*5 = 30
%e A193873 a(2) =  3*5*7 = 105
%e A193873 a(3) =  7*13*19 = 1729
%e A193873 a(4) =  5*13*17 = 1105
%e A193873 a(5) = 11*31*41 = 13981
%o A193873 (PARI) a(n)=my(p,q,k=1);while(!isprime(k+=n),);p=k;while(!isprime(k+=n),);q=k;while(!isprime(k+=n),);p*q*k \\ _Charles R Greathouse IV_, Sep 03 2011
%Y A193873 Cf. A001235, A077316, A092609, A121940, A154729, A193869.
%K A193873 nonn,easy
%O A193873 1,1
%A A193873 _Omar E. Pol_, Sep 02 2011

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