A190650 Product of iterated integral part of square root.

1, 2, 3, 8, 10, 12, 14, 16, 27, 30, 33, 36, 39, 42, 45, 128, 136, 144, 152, 160, 168, 176, 184, 192, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 686, 700, 714, 728, 742, 756, 770, 784, 798, 812, 826, 840, 854, 868, 882, 1024, 1040, 1056, 1072, 1088, 1104, 1120, 1136, 1152, 1168, 1184, 1200, 1216, 1232, 1248, 1264, 1280

Offset

1,2

Comments

a(n) = n * f(n) * f(f(n)) * ..., where f(n) = floor(sqrt(n)). Although this is written as an infinite product, all but finitely many terms are 1.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1; for n>1, a(n) = n*a(floor(sqrt(n))).

a(n) <= n^2/2 for n > 1. Equality holds for n = 2^2^k.

Example

a(1) = 1, a(2) = 2*1, a(3) = 3*1, a(4) = 4*2*1, a(5) = 5*2*1, ....

Prog

(PARI) a(n)=local(r); r=n; while((n=sqrtint(n))>1, r*=n); r

Crossrefs

Cf. A000196, A007590, A001146, A190668.

Sequence in context: A028751 A325424 A057543 * A000059 A340301 A216761

Adjacent sequences: A190647 A190648 A190649 * A190651 A190652 A190653

Keyword

nonn,easy

Author

Franklin T. Adams-Watters, May 16 2011

Status

approved