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Beginning with 1, the smallest number not included earlier such that the n-th partial product is an n-th power; or the geometric mean of the first n terms is an integer.

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`%I #11 Jun 03 2015 17:23:48
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`%S 1,4,2,32,128,8,1024,16,8192,32768,64,262144,1048576,256,8388608,512,
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`%T 67108864,268435456,2048,2147483648,4096,17179869184,68719476736,
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`%U 16384,549755813888,2199023255552,65536,17592186044416,131072,140737488355328
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`%N Beginning with 1, the smallest number not included earlier such that the n-th partial product is an n-th power; or the geometric mean of the first n terms is an integer.
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`%C Every term is a power of 2 and the geometric mean of first n terms is 2 for n >1. Rearrangement of powers of 2.
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`%F a(n) = 2^A002251(n-1). - _David Wasserman_, Mar 07 2005
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`%e a(5) = 128: the product of the first five terms is 1*4*2*32*128 = 2^15 = 8^5; 4 gives 4^5, also a 5th power, but 4 is already included.
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`%o (PARI) v=[1];n=1;while(n<10^4,p=n*prod(i=1,#v,v[i]);if(ispower(p,#v+1)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=1);n++);v \\ _Derek Orr_, May 27 2015
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`%Y Cf. A002251.
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`%K nonn
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`%O 1,2
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`%A _Amarnath Murthy_, Jul 26 2003
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`%E More terms from _David Wasserman_, Mar 07 2005
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