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A176878
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Numbers that are the product of 3 distinct primes a, b and c, such that a^2 + b^2 + c^2 is prime.
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2
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105, 231, 273, 345, 357, 399, 483, 561, 627, 651, 663, 705, 759, 777, 795, 903, 957, 969, 987, 1005, 1023, 1131, 1173, 1221, 1239, 1281, 1353, 1407, 1419, 1491, 1533, 1551, 1581, 1605, 1659, 1677, 1743, 1749, 1887, 2013, 2037, 2055, 2091, 2121, 2139
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OFFSET
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1,1
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LINKS
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EXAMPLE
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105 = 3*5*7; 3^2 + 5^2 + 7^2 = 83.
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MATHEMATICA
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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
Take[Union[Times@@@Select[Subsets[Prime[Range[50]], {3}], PrimeQ[Total[#^2]]&]], 50] (* Harvey P. Dale, Mar 11 2011 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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