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A163299
a(n) = (the number of divisors of n)^(the binary order of n).
1
1, 2, 4, 9, 8, 64, 8, 64, 81, 256, 16, 1296, 16, 256, 256, 625, 32, 7776, 32, 7776, 1024, 1024, 32, 32768, 243, 1024, 1024, 7776, 32, 32768, 32, 7776, 4096, 4096, 4096, 531441, 64, 4096, 4096, 262144, 64, 262144, 64, 46656, 46656, 4096, 64, 1000000
OFFSET
1,2
COMMENTS
The binary order of n is ceiling(log_2(n)).
LINKS
FORMULA
a(n) = A000005(n)^A029837(n).
EXAMPLE
a(1)=1^0=1. a(2)=2^1=2, a(3)=2^2=4.
MAPLE
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
MATHEMATICA
Table[DivisorSigma[0, n]^(Ceiling[Log[2, n]]), {n, 100}] (* G. C. Greubel, Dec 18 2016 *)
PROG
(PARI) main(size)={return(vector(size, n, (numdiv(n))^(ceil(log(n)/ log(2))))); } \\ Anders Hellström, Jul 13 2015
CROSSREFS
Sequence in context: A103147 A340169 A079781 * A337911 A198679 A244285
KEYWORD
nonn,base,less
AUTHOR
EXTENSIONS
Examples corrected by R. J. Mathar, Oct 10 2009
STATUS
approved