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

Author

Jonathan Vos Post, Apr 11 2008

Keywords

• easy
• nonn

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

Crossrefs

Cf. A000040, A000312, A068145, A133664, A136292

Programs

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

Formula

A000040 INTERSECTION {A000312(a) + A000312(b) + A000312(c) + A000312(d) + A000312(e) + A000312(f)}.