

A086482


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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(n1).  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: A317899 A076936 A303085 * A078758 A102015 A302890
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



