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%I #6 May 13 2013 01:54:09
%S 41,47,61,67,113,139,293,313,571,797,823,1307,3191,3391,3463,3643,
%T 3947,4153,6257,6263,6793,7019,9433,12757,15629,15881,46687,46919,
%U 46997,47681,49811,49843,50069,50321,53419,56039,56543,59183,93319
%N Primes of the form a^a + b^b + c^c + d^d + e^e + f^f.
%H A136294 Charles R Greathouse IV, <a href="/A136294/b136294.txt">Table of n, a(n) for n = 1..10000</a>
%F A000040 INTERSECTION {A000312(a) + A000312(b) + A000312(c) + A000312(d) + A000312(e) + A000312(f)}.
%e a(1) = 41 = 1^1 + 1^1 + 2^2 + 2^2 + 2^2 + 3^3.
%e a(2) = 47 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^3.
%e a(3) = 61 = 1^1 + 1^1 + 1^1 + 2^2 + 3^3 + 3^3.
%e a(4) = 67 = 1^1 + 2^2 + 2^2 + 2^2 + 3^3 + 3^3.
%e a(5) = 113 = 1^1 + 2^2 + 3^3 + 3^3 + 3^3 + 3^3.
%t Select[Union[ Flatten[Table[ a^a + b^b + c^c + d^d + e^e + f^f, {a, 1, 20}, {b, 1, a}, {c, 1, b}, {d, 1, c}, {e, 1, d}, {f, 1, e}]]], PrimeQ]
%o (PARI) v=[]; for(a=1, 30, for(b=1, a, for(c=1, b, for(d=1, c, for(e=1, d, for(f=1, e, if(ispseudoprime(t=a^a+b^b+c^c+d^d+e^e+f^f), v=concat(v, t)))))))); #v \\ _Charles R Greathouse IV_, Feb 15 2011
%Y Cf. A000040, A000312, A068145, A133664, A136292
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Apr 11 2008
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