

A190650


Product of iterated integral part of square root.


2



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
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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


AUTHOR

Franklin T. AdamsWatters, May 16 2011


STATUS

approved



