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A189151
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Numbers n such that n < floor(sqrt(n)) * ceiling(sqrt(n)).
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4
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5, 10, 11, 17, 18, 19, 26, 27, 28, 29, 37, 38, 39, 40, 41, 50, 51, 52, 53, 54, 55, 65, 66, 67, 68, 69, 70, 71, 82, 83, 84, 85, 86, 87, 88, 89, 101, 102, 103, 104, 105, 106, 107, 108, 109, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 145, 146, 147, 148
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OFFSET
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1,1
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COMMENTS
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n belongs to this sequence iff
n in (k^2,k*(k+1)), k >= 0.
See also:
n = floor(sqrt(n))*ceiling(sqrt(n)), i.e.
n = k^2 or n = k*(k+1), k >= 0.
n > floor(sqrt(n))*ceiling(sqrt(n)), i.e.
n in (k*(k+1),k^2), k >= 0.
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LINKS
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FORMULA
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G.f.: (1-x)^(-2)-(1-x)^(-1)*(1+x+x^2-Sum_{k>=0} k*x^((k^2-5*k+8)/2)). - Robert Israel, Jan 02 2017
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MAPLE
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MATHEMATICA
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Select[Range[200], # < Floor[Sqrt[#]] Ceiling[Sqrt[#]] &] (* T. D. Noe, Apr 20 2011 *)
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PROG
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(Python)
from itertools import count, islice
def A189151_gen(): # generator of terms
return (n for k in count(0) for n in range(k**2+1, k*(k+1)))
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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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