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%I #16 Dec 19 2016 06:15:52
%S 1,2,4,9,8,64,8,64,81,256,16,1296,16,256,256,625,32,7776,32,7776,1024,
%T 1024,32,32768,243,1024,1024,7776,32,32768,32,7776,4096,4096,4096,
%U 531441,64,4096,4096,262144,64,262144,64,46656,46656,4096,64,1000000
%N a(n) = (the number of divisors of n)^(the binary order of n).
%C The binary order of n is ceiling(log_2(n)).
%H G. C. Greubel, <a href="/A163299/b163299.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000005(n)^A029837(n).
%e a(1)=1^0=1. a(2)=2^1=2, a(3)=2^2=4.
%p A029837 := proc(n) ceil(log[2](n)) ; end proc: A163299 := proc(n) numtheory[tau](n) ^ A029837(n) ; end proc: seq(A163299(n),n=1..100) ; # _R. J. Mathar_, Oct 10 2009
%t Table[DivisorSigma[0, n]^(Ceiling[Log[2, n]]), {n, 100}] (* _G. C. Greubel_, Dec 18 2016 *)
%o (PARI) main(size)={return(vector(size,n,(numdiv(n))^(ceil(log(n)/ log(2)))));} \\ _Anders Hellström_, Jul 13 2015
%Y Cf. A000005, A029837.
%K nonn,base,less
%O 1,2
%A _Juri-Stepan Gerasimov_, Jul 26 2009
%E Examples corrected by _R. J. Mathar_, Oct 10 2009
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