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 A300287 a(n) = floor((1/n) * Sum_{k=1..n} sqrt(k)). 0
 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Table of n, a(n) for n=1..100. Mircea Merca, On the Arithmetic Mean of the Square Roots of the First n Positive Integers, The College Mathematics Journal, Vol. 48, No. 2 (March 2017), pp. 129-133. S. Ramanujan, On the sum of the square roots of the first n natural numbers, Journal of the Indian Mathematical Society, VIII (1915), pp. 173-175. Thomas P. Wihler, Rounding the arithmetic mean value of the square roots of the first n integers, arXiv:1803.00362 [math.NT], 2018. FORMULA a(n) = floor((2/3)*sqrt(n+1)*(1+1/(4*n))). See Theorem 1 of Wihler paper. MATHEMATICA Table[Floor[1/n Sum[Sqrt[k], {k, n}]], {n, 200}] (* Vincenzo Librandi, Mar 02 2018 *) PROG (PARI) a(n) = floor(sum(k=1, n, sqrt(k))/n); (Magma) [Floor(&+[Sqrt(k)/n: k in [1..n]]): n in [1..100]]; // Bruno Berselli, Mar 02 2018 CROSSREFS Cf. A025224. Sequence in context: A263206 A230501 A287272 * A226764 A344420 A206244 Adjacent sequences: A300284 A300285 A300286 * A300288 A300289 A300290 KEYWORD nonn AUTHOR Michel Marcus, Mar 02 2018 STATUS approved

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Last modified September 25 15:00 EDT 2023. Contains 365648 sequences. (Running on oeis4.)