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%I #3 Mar 31 2012 12:38:26
%S 4357,12101,16901,28901,52901,164837,184901,220901,224677,417317,
%T 427717,682277,792101,820837,894917,972197,1020101,1110917,1136357,
%U 1144901,1223237,1313317,1552517,1887877,1943237,1976837,2056357,2464901
%N Primes of the form 1+A162143(k).
%C Primes p such that p-1 equals the square of a product of three distinct primes.
%C Primes of the similar form A162143(k)-1 do not exist, because A162143 are squares
%C which allows for the obvious factorization A162143(k)-1 = (A007304(k)+1)*(A007304(k)-1).
%e For p=4357=a(1), p=14356=2^2*3^2*11^2. For p=12101, p=1=12100=2^2*5^2*11^2.
%t f[n_]:=FactorInteger[n][[1,2]]==2&&Length[FactorInteger[n]]==3&&FactorInteger[n][[2, 2]]==2&&FactorInteger[n][[3,2]]==2; lst={};Do[p=Prime[n];If[f[p-1], AppendTo[lst,p]],{n,2,9!}];lst
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Aug 14 2009
%E Edited by _R. J. Mathar_, Aug 18 2009
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