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

Author

Franklin T. Adams-Watters, May 16 2011

Keywords

• nonn
• easy

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.

Examples

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

Links

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

Crossrefs

Cf. A000196, A007590, A001146, A190668.

Programs

PARI

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

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.