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a(n) = n^sopf(n), where sopf(n) is the sum of the distinct primes dividing n (A008472).
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%I #7 Jul 10 2012 12:22:43

%S 1,4,27,16,3125,7776,823543,64,729,10000000,285311670611,248832,

%T 302875106592253,20661046784,2562890625,256,827240261886336764177,

%U 1889568,1978419655660313589123979,1280000000,16679880978201

%N a(n) = n^sopf(n), where sopf(n) is the sum of the distinct primes dividing n (A008472).

%H T. D. Noe, <a href="/A176147/b176147.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = n^A008472(n).

%e a(1) = 1^0 = 1;

%e a(2) = 2^2 = 4;

%e a(3) = 3^3 = 27;

%e a(4) = 4^2 = 16.

%t Table[n^Total[Transpose[FactorInteger[n]][[1]]], {n, 20}]

%Y Cf. A008472.

%K nonn

%O 1,2

%A _Michel Lagneau_, Apr 10 2010