login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A061592 Smallest number >= n whose product of divisors is an n-th power. 1
1, 6, 4, 24, 16, 8, 64, 120, 36, 16, 1024, 216, 4096, 128, 32, 840, 65536, 256, 262144, 1680, 64, 2048, 4194304, 216, 1296, 4096, 900, 128, 268435456, 5040, 1073741824, 7560, 2048, 65536, 5184, 256, 68719476736, 524288, 4096, 15120, 1099511627776 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= 2^(A011772(n)). If p > 2 is prime, then a(p) = 2^(p-1). - Chai Wah Wu, Mar 13 2016

If p == 1 mod 4 and prime, then a(2p) = 2^(p-1). If p == 3 mod 4 and prime, then a(2p) = 2^p. - Chai Wah Wu, Mar 30 2016

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Min{x|Product[divisors of x] = s^n} = Min{x|A007955(x) = s^n}

EXAMPLE

n = 31: a(31) = 2^30 since Apply[Times, Divisors[2^30]] = 32768^31. n = 50: a(50) = 1296 because the product of 25 divisors is (6^4)^(25/2) = 6^50.

CROSSREFS

Cf. A007955.

Sequence in context: A120462 A236602 A169689 * A081631 A137174 A129886

Adjacent sequences:  A061589 A061590 A061591 * A061593 A061594 A061595

KEYWORD

nonn

AUTHOR

Labos Elemer, May 22 2001

EXTENSIONS

More terms from David Wasserman, Jun 19 2002

Definition clarified by Chai Wah Wu, Mar 13 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 15 18:46 EST 2019. Contains 319168 sequences. (Running on oeis4.)