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A320471
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a(n) = floor(sqrt(n)) mod ceiling(sqrt(n)).
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1
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0, 1, 1, 0, 2, 2, 2, 2, 0, 3, 3, 3, 3, 3, 3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 9, 9, 9, 9, 9, 9
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OFFSET
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1,5
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COMMENTS
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Sequence consists of zeros interleaved with the positive integers, each positive integer k appearing 2k times.
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LINKS
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Table of n, a(n) for n=1..87.
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FORMULA
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a(n) = A000196(n) - A037213(n).
a(n) = A000196(n)*A049240(n).
a(n) = A000196(n) mod A003059(n).
a(n) = (n - A173517(n)) - A037213(n)^2.
a(n) = binomial(ceiling(sqrt(n)),floor(sqrt(n))) - 1.
From David A. Corneth, Nov 04 2018: (Start)
a(k^2) = 0.
a(m) = floor(sqrt(m)) for nonsquare m. (End)
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MAPLE
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a:= proc(n) modp(floor(sqrt(n)), ceil(sqrt(n))) end: seq(a(n), n=1..100); # Muniru A Asiru, Oct 17 2018
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MATHEMATICA
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Array[Mod[Floor@ #, Ceiling@ #] &@ Sqrt@ # &, 99] (* or *)
Array[IntegerPart@ # - If[IntegerQ@ #, #, 0] &@ Sqrt@ # &, 99] (* or *)
Flatten@ Array[{0}~Join~ConstantArray[#, 2 #] &, 9] (* Michael De Vlieger, Oct 15 2018 *)
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PROG
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(PARI) a(n) = sqrtint(n) % (1+sqrtint(n-1)); \\ Michel Marcus, Nov 04 2018
(PARI) a(n) = sqrtint(n-1) * !issquare(n) \\ David A. Corneth, Nov 04 2018
[Binomial(Ceiling(Sqrt(n)), Floor(Sqrt(n))) - 1: n in [1..100]]; // Vincenzo Librandi, Dec 02 2018
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CROSSREFS
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Cf. A000196, A003059, A037213, A049240, A173517.
Sequence in context: A305629 A214664 A214666 * A333180 A127444 A241477
Adjacent sequences: A320468 A320469 A320470 * A320472 A320473 A320474
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KEYWORD
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nonn
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AUTHOR
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Kritsada Moomuang, Oct 13 2018
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EXTENSIONS
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Corrected by Michel Marcus, Jun 14 2022
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STATUS
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approved
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