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%I #3 Mar 30 2012 18:36:04
%S 1859,357911,2141399,4641629,6633419,8447039,10338119,13526009,
%T 20163059,21603425,24099569,26187119,26483321,28226549,33379569,
%U 33485139,40790009,50139819,52046075,56152179,57170075,59824925,72541799
%N Integers of the form p^2*q in A120806: x+d+1 is prime for all divisors d of x. Both p and q are odd primes, with p and q distinct. See A054753.
%F a(n) = n-th element of A120806 of the form p^2*q where p and q are distinct odd primes.
%e a(1)=1859 since x=11*13^2, divisors(x)={1,11,13,11*13,13^2,11*13^2} and x+d+1={1861,1871,1873,2003,2029,3719} 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; y:=simplify(x^(1/3)); if x mod 6 = 5 and not type(y,integer) #clunky and not 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, A054753.
%K nonn
%O 1,1
%A _Walter Kehowski_, Jul 06 2006
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