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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The binary order of n is ceiling(log_2(n)).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Cf. A000005, A029837.

Sequence in context: A103147 A340169 A079781 * A337911 A198679 A244285

Adjacent sequences:  A163296 A163297 A163298 * A163300 A163301 A163302

KEYWORD

nonn,base,less

AUTHOR

Juri-Stepan Gerasimov, Jul 26 2009

EXTENSIONS

Examples corrected by R. J. Mathar, Oct 10 2009

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)