

A061592


Smallest number >= n whose product of divisors is an nth 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
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OFFSET

1,2


COMMENTS

a(n) <= 2^(A011772(n)). If p > 2 is prime, then a(p) = 2^(p1).  Chai Wah Wu, Mar 13 2016
If p == 1 mod 4 and prime, then a(2p) = 2^(p1). 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{xProduct[divisors of x] = s^n} = Min{xA007955(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



