login
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
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.
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 26 2003
EXTENSIONS
More terms from David Wasserman, Mar 07 2005
STATUS
approved