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

1,2

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.

Links

Table of n, a(n) for n=1..30.

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A002251.

Sequence in context: A344536 A348567 A303085 * A078758 A364878 A102015

Adjacent sequences: A086479 A086480 A086481 * A086483 A086484 A086485

Keyword

nonn

Author

Amarnath Murthy, Jul 26 2003

Extensions

More terms from David Wasserman, Mar 07 2005

Status

approved