A190668 a(n) = Product_{k>=1} floor(n^(1/k)).

1, 2, 3, 8, 10, 12, 14, 32, 54, 60, 66, 72, 78, 84, 90, 256, 272, 288, 304, 320, 336, 352, 368, 384, 500, 520, 810, 840, 870, 900, 930, 1920, 1980, 2040, 2100, 2592, 2664, 2736, 2808, 2880, 2952, 3024, 3096, 3168, 3240, 3312, 3384, 3456, 4116, 4200, 4284, 4368, 4452, 4536, 4620, 4704, 4788, 4872, 4956, 5040, 5124, 5208, 5292, 16384, 16640, 16896, 17152, 17408, 17664, 17920, 18176, 18432, 18688, 18944, 19200, 19456, 19712, 19968, 20224, 20480

Offset

1,2

Comments

Although written as an infinite product, all but finitely many terms in the product are 1.

Links

Table of n, a(n) for n=1..80.

Formula

a(n) < n^log(n) for n > 4.

Example

a(8) = 8 * floor(sqrt(8)) * floor(8^(1/3)) * 1 * ... = 8 * 2 * 2 * 1 * ... = 32.

Prog

(PARI) a(n)=prod(k=1, floor(log(n+1/2)/log(2)), floor(sqrtn(n+1/2, k)))

Crossrefs

Cf. A190650, A006218, A061567.

Sequence in context: A216761 A276559 A097053 * A250037 A360940 A132327

Adjacent sequences: A190665 A190666 A190667 * A190669 A190670 A190671

Keyword

nonn

Author

Franklin T. Adams-Watters, May 16 2011

Status

approved