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 A320471 a(n) = floor(sqrt(n)) mod ceiling(sqrt(n)). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Sequence consists of zeros interleaved with the positive integers, each positive integer k appearing 2k times. LINKS FORMULA 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) MAPLE a:= proc(n) modp(floor(sqrt(n)), ceil(sqrt(n))) end: seq(a(n), n=1..100); # Muniru A Asiru, Oct 17 2018 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000196, A003059, A037213, A049240, A173517. Sequence in context: A305629 A214664 A214666 * A333180 A127444 A241477 Adjacent sequences:  A320468 A320469 A320470 * A320472 A320473 A320474 KEYWORD nonn AUTHOR Kritsada Moomuang, Oct 13 2018 EXTENSIONS Corrected by Michel Marcus, Jun 14 2022 STATUS approved

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Last modified July 7 02:44 EDT 2022. Contains 355141 sequences. (Running on oeis4.)