A136294 Primes of the form a^a + b^b + c^c + d^d + e^e + f^f.
41, 47, 61, 67, 113, 139, 293, 313, 571, 797, 823, 1307, 3191, 3391, 3463, 3643, 3947, 4153, 6257, 6263, 6793, 7019, 9433, 12757, 15629, 15881, 46687, 46919, 46997, 47681, 49811, 49843, 50069, 50321, 53419, 56039, 56543, 59183, 93319
Offset: 1
Examples
a(1) = 41 = 1^1 + 1^1 + 2^2 + 2^2 + 2^2 + 3^3. a(2) = 47 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^3. a(3) = 61 = 1^1 + 1^1 + 1^1 + 2^2 + 3^3 + 3^3. a(4) = 67 = 1^1 + 2^2 + 2^2 + 2^2 + 3^3 + 3^3. a(5) = 113 = 1^1 + 2^2 + 3^3 + 3^3 + 3^3 + 3^3.
Links
- A136294 Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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] -
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