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%I #10 Mar 02 2015 02:19:00
%S 105,231,273,345,357,399,483,561,627,651,663,705,759,777,795,903,957,
%T 969,987,1005,1023,1131,1173,1221,1239,1281,1353,1407,1419,1491,1533,
%U 1551,1581,1605,1659,1677,1743,1749,1887,2013,2037,2055,2091,2121,2139
%N Numbers that are the product of 3 distinct primes a, b and c, such that a^2 + b^2 + c^2 is prime.
%e 105 = 3*5*7; 3^2 + 5^2 + 7^2 = 83.
%t l[n_]:=Last/@FactorInteger[n]; f[n_]:=First/@FactorInteger[n]; lst={};Do[If[l[n]=={1,1,1},a=f[n][[1]];b=f[n][[2]];c=f[n][[3]];If[PrimeQ[a^2+b^2+c^2],AppendTo[lst,n]]],{n,7!}];lst
%t Take[Union[Times@@@Select[Subsets[Prime[Range[50]],{3}],PrimeQ[Total[#^2]]&]],50] (* _Harvey P. Dale_, Mar 11 2011 *)
%o (PARI) lst(lim)=my(v=List());forprime(a=3,lim^(1/3),forprime(b=a+2,sqrt(lim\a),forprime(c=b+2,lim\(a*b),if(isprime(a^2+b^2+c^2),listput(v,a*b*c)))));vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Mar 11 2011
%Y Cf. A006881, A014574, A176875, A176876, A176877.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Apr 27 2010
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