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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
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
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
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