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%I #6 Nov 04 2013 13:01:50
%S 0,1,2,3,4,5,6,7,8,9,16,32,64,128,256,512,729,2187,6561,19683,65536,
%T 262144,390625,1953125,10077696,40353607,134217728,387420489,
%U 402653184,536870912,671088640,805306368,939524096,1073741824,1207959552,1549681956,1937102445
%N Numbers that set records in A133500.
%H N. J. A. Sloane, <a href="/A133504/b133504.txt">Table of n, a(n) for n = 1..81</a>
%e Factored forms are 0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2^4, 2^5, 2^6, 2^7, 2^8, 2^9, 3^6, 3^7, 3^8, 3^9, 2^16, 2^18, 5^8, 5^9, 2^9*3^9, 7^9, 2^27, 3^18, 2^27*3, 2^29, 2^27*5, 2^28*3, 2^27*7, 2^30, 2^27*3^2, 2^2*3^18, 3^18*5,
%e 2*3^19, 3^18*7, 2^3*3^18, 3^20, 2^4*3^18, 2^5*3^18, 2^6*3^18, 2^7*3^18, 2^8*3^18, 2^9*3^18, 3^24, 2^27*3^7, 3^25, 2^27*3^8, 3^26, 2^27*3^9, 3^27, 2^43, 2^16*3^18, 2^45, 2^18*3^18, 3^18*5^8, 2^27*5^9, ...
%p M:=100000; t1:=[]; t2:=[]; rec:=-1; for n from 0 to M do m:=powertrain(n); if m > rec then rec:=m; t1:=[op(t1),m]; t2:=[op(t2),n]; fi; od: lprint(t1); lprint(t2);
%Y Cf. A133500, A133505.
%K nonn
%O 1,3
%A _J. H. Conway_ and _N. J. A. Sloane_, Dec 03 2007
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