%I M0593 N0214 #23 Feb 02 2022 00:06:49

%S 1,2,3,4,9,27,512,134217728

%N An exponential function on partitions (next term is 2^512).

%C Largest number that can be expressed in the form a_1 ^ a_2 ^ ... ^ a_k, where a_1 + a_2 + ... + a_k = n. - _Franklin T. Adams-Watters_, Apr 09 2010

%C Equivalently, largest number that can be expressed using the constant 1 exactly n times with only addition and exponentiation -- no concatenation of digits is allowed. (Comment to facilitate searching.) - _Rick L. Shepherd_, Jun 14 2017

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H S. W. Golomb and Judith Richman, <a href="https://www.jstor.org/stable/2317895">Problem E2118</a>, Amer. Math. Monthly, 76 (1969), 830-831.

%F For n >= 7, a(n) = 2^a(n-2). - _Franklin T. Adams-Watters_, Apr 09 2010

%Y Cf. A000792, A014221. - _Franklin T. Adams-Watters_, Apr 09 2010

%K nonn

%O 1,2

%A _N. J. A. Sloane_