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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 (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

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