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%I #3 Mar 30 2012 18:36:04
%S 935,305015,2339315,3690185,14080121,14259629,16143005,17754869,
%T 18679409,26655761,29184749,47372135,80945699,82768529,87102509
%N Integers of the form p*q*r in A120806: x+d+1 is prime for all divisors d of x, where p, q and r are distinct odd primes. See A007304.
%F a(n) = n-th element of A120806 of the form p*q*r where p, q and r are distinct odd primes.
%e a(1)=935 since x=5*11*17, divisors(x)={1,5,11,17,5*11,5*17,11*17,5*11*17} and x+d+1={937, 941, 947, 953, 991, 1021, 1123, 1871} are all prime.
%p with(numtheory); is3almostprime := proc(n) local L; if n in [0,1] or isprime(n) then return false fi; L:=ifactors(n)[2]; if nops(L) in [1,2,3] and convert(map(z-> z[2], L), `+`) = 3 then return true else return false fi; end; L:=[]: for w to 1 do for k from 1 while nops(L)<=50 do x:=2*k+1; if x mod 6 = 5 and issqrfree(x) and is3almostprime(x) and andmap(isprime,[x+2,2*x+1]) then S:=divisors(x); Q:=map(z-> x+z+1, S); if andmap(isprime,Q) then L:=[op(L),x]; print(nops(L),ifactor(x)); fi; fi; od od;
%Y Cf. A120806, A007304, A120809, A120808, A120807.
%K nonn
%O 1,1
%A _Walter Kehowski_, Jul 06 2006
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