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 A190650 Product of iterated integral part of square root. 2

%I

%S 1,2,3,8,10,12,14,16,27,30,33,36,39,42,45,128,136,144,152,160,168,176,

%T 184,192,250,260,270,280,290,300,310,320,330,340,350,432,444,456,468,

%U 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

%N Product of iterated integral part of square root.

%C 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.

%H Rémy Sigrist, <a href="/A190650/b190650.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

%Y Cf. A000196, A007590, A001146, A190668.

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, May 16 2011

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