A061592 Smallest number >= n whose product of divisors is an n-th power.

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

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: A236602 A169689 A328757 * 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