A086482 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.

1, 4, 2, 32, 128, 8, 1024, 16, 8192, 32768, 64, 262144, 1048576, 256, 8388608, 512, 67108864, 268435456, 2048, 2147483648, 4096, 17179869184, 68719476736, 16384, 549755813888, 2199023255552, 65536, 17592186044416, 131072, 140737488355328

Offset: 1

Author

Amarnath Murthy, Jul 26 2003

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A002251.

Programs

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

Formula

a(n) = 2^A002251(n-1). - David Wasserman, Mar 07 2005

Extensions

More terms from David Wasserman, Mar 07 2005