A061592 - OEIS

%I #11 Mar 30 2016 22:59:25

%S 1,6,4,24,16,8,64,120,36,16,1024,216,4096,128,32,840,65536,256,262144,

%T 1680,64,2048,4194304,216,1296,4096,900,128,268435456,5040,1073741824,

%U 7560,2048,65536,5184,256,68719476736,524288,4096,15120,1099511627776

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

%C a(n) <= 2^(A011772(n)). If p > 2 is prime, then a(p) = 2^(p-1). - _Chai Wah Wu_, Mar 13 2016

%C 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

%H Chai Wah Wu, <a href="/A061592/b061592.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 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.

%Y Cf. A007955.

%K nonn

%O 1,2

%A _Labos Elemer_, May 22 2001

%E More terms from _David Wasserman_, Jun 19 2002

%E Definition clarified by _Chai Wah Wu_, Mar 13 2016