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A190650
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Product of iterated integral part of square root.
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2
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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
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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.
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EXAMPLE
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a(1) = 1, a(2) = 2*1, a(3) = 3*1, a(4) = 4*2*1, a(5) = 5*2*1, ....
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PROG
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(PARI) a(n)=local(r); r=n; while((n=sqrtint(n))>1, r*=n); r
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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