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A025224 a(n) = floor(Sum_{k=1..n} sqrt(k)). 10
0, 1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 29, 32, 36, 40, 44, 48, 52, 57, 61, 66, 70, 75, 80, 85, 90, 95, 101, 106, 112, 117, 123, 129, 134, 140, 146, 152, 159, 165, 171, 178, 184, 191, 197, 204, 211, 218, 224, 231, 239, 246, 253, 260, 268, 275, 282, 290, 298, 305, 313, 321, 329, 337 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Shekatkar took Ramanujan's formula for sum of the square roots of first n natural numbers, and generalized to include r-th roots where r is any real number greater than 1, using simple properties of Riemann integrable functions. - Jonathan Vos Post, Apr 05 2012

LINKS

Table of n, a(n) for n=0..63.

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.

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.

Snehal Shekatkar, On the sum of the r'th roots of first n natural numbers, arXiv:1204.0877 [math.NT], 2012-2013.

FORMULA

a(n) ~= floor ((4n + 3)sqrt(n)/6 - exp(-Pi / 2)). - Charles R Greathouse IV, Jul 29 2007. Corrected by Carl R. White, Jan 22 2009

MAPLE

A025224:= proc(i)

local a, n;

a:=0;

for n from 1 to i do  a:=a+sqrt(n); print(floor(a)); od; end:

A025224(10000);  # Paolo P. Lava, Jan 08 2013

MATHEMATICA

s=0; lst={}; Do[s+=Sqrt[n]; AppendTo[lst, c=Floor[s]], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 06 2010 *)

Floor@HarmonicNumber[Range[0, 30], -1/2] (* Vladimir Reshetnikov, Nov 07 2015 *)

PROG

(PARI) a(n) = floor(sum(k=0, n, sqrt(k))); \\ Michel Marcus, Mar 01 2016

CROSSREFS

Cf. A022554.

Sequence in context: A130798 A165453 A282168 * A294023 A096182 A186347

Adjacent sequences:  A025221 A025222 A025223 * A025225 A025226 A025227

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 21 06:35 EDT 2021. Contains 347596 sequences. (Running on oeis4.)