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A259227
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Hydropronic numbers: numbers n that can be written as a product of 2 integers whose sum is equal to ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(n)).
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1
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1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 66, 70, 72, 77, 80, 81, 84, 88, 90, 91, 96, 99, 100, 104, 108, 110, 112, 117, 120, 121, 126, 130, 132, 135, 140, 143, 144, 150, 154, 156, 160
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OFFSET
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1,2
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COMMENTS
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It appears that ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(n)) is A027434(n).
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LINKS
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MATHEMATICA
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Select[Range@160, IntegerQ@Sqrt[((r = Ceiling@Sqrt@#) + Ceiling[#/r])^2 - 4 #] &] (* Ivan Neretin, Oct 16 2016 *)
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PROG
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(PARI) isok(n) = {d = divisors(n); for (k=1, #d, if ((d[k] + n/d[k]) == ceil(n/ceil(sqrt(n)))+ceil(sqrt(n)), return (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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